(a) MLE of $\lambda$ is obtained by maximizing the log-likelihood. Suppose that X1,X2,…,XnX1,X2,…,Xn are independent and identically distributed exponential random variables with parameter λ, then the probability density function of XiXi is given by $$f(x_i;\lambda) =\lambda e^ {-\lambda x_i}, \quad x_i\geq0. $$
The log-likelihood function is given by$$\begin{aligned}\ln L(\lambda) &= \ln (\lambda^n e^{-\lambda(x_1+x_2+\cdots+x_n)}) \\&=n\ln \lambda-\lambda(x_1+x_2+\cdots+x_n).\end{aligned}$$
The first derivative of the log-likelihood function with respect to λλ is$$\frac {d\ln L(\lambda)} {d\lambda} = \frac{n}{\lambda}-x_1-x_2-\cdots-x_n.$$
The first derivative is zero when $$\frac{n}{\lambda}-\sum_{i=1} ^{n} x_i=0. $$Hence, the MLE of λλ is $$\hat{\lambda} =\frac{n}{\sum_{i=1} ^{n} x_i}. $$
Substituting the value of $\hat{\lambda} $ gives the maximum value of the log-likelihood. So, the MLE of $\lambda$ is given by $$\boxed{\hat{\lambda} =\frac{n}{\sum_{i=1} ^{n} x_i}}. $$
The MLE of $\lambda$ is $\frac {3} {\sum_{i=1} ^{n} x_i}$.
(b) The median of the exponential distribution is given by$$m = \frac {\ln (2)} {\lambda}. $$
Therefore, the log-likelihood function for median is given by$$\begin{aligned}\ln L(m) &= \sum_{i=1}^{n} \ln f(x_i;\lambda)\\&= \sum_{i=1}^{n} \ln \left(\frac{1}{\lambda}e^{-x_i/\lambda}\right)\\&= -n\ln\lambda-\frac{1}{\lambda}\sum_{i=1}^{n}x_i.\end{aligned}$$
The first derivative of the log-likelihood function with respect to mm is$$\frac {d\ln L(m)} {dm} = \frac {1} {\lambda}-\frac {1} {\lambda^2} \sum_{i=1} ^{n}x_i\ln 2. $$
The first derivative is zero when $$\frac {1} {\lambda} =\frac{1}{\lambda^2}\sum_{i=1}^{n}x_i\ln 2.$$Hence, the MLE of mm is $$\boxed{\hat{m} = \frac{\ln 2}{\bar{x}}}.$$where $\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i.$Therefore, the MLE of m is $\frac {\ln 2} {\bar{x}}. $
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X^2-2(x+5)
Help me PLSSS
Answer:
hope this helpss
Step-by-step explanation:
Answer:
Step-by-step explanation:
if you have to simplify it then distribute -2
x²-2(x+5)=x²-2x-10
if problem is as mentioned by other answerer,then
[tex]\frac{d}{dx} (x^2-2(x+5))=-2\\x^2-2x-10= \int (-2dx)+c\\x^2-2x-10=-2x+c\\x^2=c+10\\x=\pm \sqrt{c+10}[/tex]
Solve for the values of x and y.
Answer:
x = 20
y = 7.2
Step-by-step explanation:
12/x = 9/15
9x = 180
x = 20
12/x= y/12
12/20 = y/12
144 = 20y
y = 7.2
y = 20
Which point is found on the line represented by the equation y+6=x ?
A (−5,1)
B (2,−4)
C (3,9)
D (6,6)
The point that satisfies the equation y+6=x is :
A (−5,1)
The line represented by the equation y+6 = x can be rewritten as x - y = -6. The equation is in the standard form:
Ax + By = C.
The x-intercept and y-intercept can be found using the standard form. Then, plot these points on the graph and draw a straight line between them to complete the graph of the equation.
Using the equation x - y = -6 to find the x-intercept, set y = 0 and solve for x.
Thus, x - 0 = -6x = -6
The x-intercept of the line is (-6, 0).
Using the equation x - y = -6 to find the y-intercept, set x = 0 and solve for y.
Thus, 0 - y = -6y = 6
The y-intercept of the line is (0, 6).
Plot the x-intercept (-6,0) and the y-intercept (0,6) on the coordinate plane. Then, draw the line through these points.
Now, we need to find which point is found on the line represented by the equation y+6 = x.
We can now plug in the values of the points to the equation:
y + 6 = x
x - y = -6(-5) - 1 = -6
The point A (-5,1) satisfies the equation since x - y = -6.
So, the answer is A (−5,1).
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You purchase a new flat screen TV for $878.99. You are charged sales tax at a rate of 6%. What is your total balance due when you go to pay for the TV?
Answer:
Sales tax: $52.74
■ Cost/Price before ST: $878.99
■ Total Cost/Price including ST: $931.73
Step-by-step explanation:
WILL GIVE BRAINLIEST PLEASE HELP ASAP, BEST ANSWER GETES BRAINLIEST. NOT A SCAM AND ITS NOT CAP WHAT SO EVER
Answer:
A. 60 + x = 90
Step-by-step explanation:
Complementary angles add up to 90 degrees so
60 + x = 90
Answer:
The answer is A: 60 + x = 90
Step-by-step explanation:
Complimentary angles are two angles that add up to 90, so the equation 60 + x = 90 is what you need to use to find the complimentary angle. I hope this helps :)
The width of a table is 2 feet less than the length. The area is 20 square feet. Find the dimensions. Show and explain all work using mathematical concepts in this module. (use quadratic equation)
Let's denote the length of the table as "x" feet. According to the problem, the width is 2 feet less than the length, so the width can be represented as "x - 2" feet. The area of the table is given as 20 square feet.
The formula for the area of a rectangle is length times width. Therefore, we can set up the equation:
Length × Width = Area
x(x - 2) = 20
Expanding the equation, we get:
x^2 - 2x = 20
Rearranging the equation in quadratic form:
x^2 - 2x - 20 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -2, and c = -20. Plugging these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4(1)(-20))) / (2(1))
Simplifying further:
x = (2 ± √(4 + 80)) / 2
x = (2 ± √84) / 2
x = (2 ± 2√21) / 2
Simplifying the expression inside the square root:
x = (1 ± √21)
So the possible values for x are 1 + √21 and 1 - √21.
Since the length cannot be negative, we take the positive value:
x = 1 + √21
Now we can find the width by substituting this value of x into the expression for width:
Width = x - 2
Width = (1 + √21) - 2
Width = -1 + √21
Therefore, the dimensions of the table are approximately 1 + √21 feet for the length and -1 + √21 feet for the width.
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You can practice on this problem. 1. A sample of men agreed to participate in a study to determine the relationship between several variables including height, weight, waste size, and percent body fat. A scatterplot with percent body fat on the y-axis and waist size (in inches) on the horizontal axis revealed a positive linear association between these variables. Computer output for the regression analysis is given below: Dependent variable is: WBE R-squared - 67.8% S - 4.713 with 250-2 - 248 degrees of freedom Variable Constant Waist Coefficient -42.734 1.70 se of coeff 2.717 0.0743 t-ratio -15.7 22.9 prob <.0001 <.0001 (a) Write the equation of the regression line (be sure to use correct notation and define your variables): (b) Explain/interpret the information provided by R-squared in the context of this problem. Be specific, (c) Calculate and interpret the correlation coefficient (r). (d) One of the men who participated in the study had waist size 35 inches and 10% body fat. Calculate the residual associated with the point for this individual.
(a) The equation of the regression line Percent Body Fat = -42.734 + 1.70 * Waist Size
(b) The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.
(c) It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.
(d) The residual associated with this point is approximately -6.766
(a) The equation of the regression line can be written as:
Percent Body Fat = -42.734 + 1.70 * Waist Size
In this equation, Percent Body Fat represents the dependent variable, Waist Size represents the independent variable, -42.734 is the intercept (constant), and 1.70 is the coefficient for the Waist Size variable.
(b) R-squared is a measure of how well the regression line fits the data. In this context, R-squared of 67.8% indicates that 67.8% of the variation in the percent body fat can be explained by the linear relationship with waist size. The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.
(c) To calculate the correlation coefficient (r), we can take the square root of the R-squared value. In this case, the correlation coefficient would be approximately √(0.678) ≈ 0.823.
Interpretation: The correlation coefficient (r) of 0.823 indicates a strong positive linear relationship between waist size and percent body fat. It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.
(d) To calculate the residual associated with the point for an individual with a waist size of 35 inches and 10% body fat, we need to substitute the waist size value into the regression equation and calculate the difference between the actual percent body fat and the predicted percent body fat.
Using the regression equation: Percent Body Fat = -42.734 + 1.70 * Waist Size
Substituting Waist Size = 35:
Percent Body Fat = -42.734 + 1.70 * 35 = -42.734 + 59.5 ≈ 16.766
The actual percent body fat for this individual is 10%. Therefore, the residual can be calculated as:
Residual = Actual Percent Body Fat - Predicted Percent Body Fat
Residual = 10 - 16.766 ≈ -6.766
The residual associated with this point is approximately -6.766. This indicates that the actual percent body fat is about 6.766 units lower than the predicted value based on the regression equation.
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81.3 x 47.5 = i am lost............
Answer:
3861.75
Step-by-step explanation:
i hope its the good answer
Each lap around the track is 400 meters. How many meters does someone run if they run 5 laps?
Answer:
2000 meters
Step-by-step explanation:
400×5=2000
Show step-by-step solution. Compute manually.
2. A salary loan of 70,000 pesos is to be repaid by equal monthly payments for 18 months. The annual interest rate is 10% compounded monthly. How much is the monthly payment?
The monthly payment for a salary loan of 70,000 pesos at a 10% annual interest rate compounded monthly for 18 months is approximately 4,530.79 pesos.
To calculate the monthly payment for the salary loan, we can use the formula for the equal payment amount in an amortizing loan:
Payment = (Principal * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-n))
Where:
Principal = 70,000 pesos (loan amount)
Monthly Interest Rate = Annual Interest Rate / 12 = 10% / 12 = 0.0083333
n = number of payments (18 months)
Let's calculate the payment amount:
Payment = (70,000 * 0.0083333) / (1 - (1 + 0.0083333)^(-18))
Payment = 4,530.79 pesos
Therefore, the monthly payment for the salary loan is approximately 4,530.79 pesos.
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A culture started with 1,000 bacteria. After 7 hours, it grew to 1.200 bacteria. Predict how many bacteria will be present after 14 hours. Round your answer to the nearest whole number.
P= Ae^kt
Answer:
8
Step-by-step explanation:
Because i wanted extra points.
on a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong?
On a 7-question multiple-choice test, with 4 answer choices for each question, we need to determine the probability of getting at least one question wrong.
To calculate the probability of getting at least one question wrong, we can consider the complementary probability, which is the probability of getting all questions correct and subtract it from 1.
The probability of getting a single question correct is 1/4, since there are 4 answer choices for each question. Therefore, the probability of getting all 7 questions correct is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = [tex](1/4)^7[/tex].
To find the probability of getting at least one question wrong, we subtract the probability of getting all questions correct from 1:
P(at least one question wrong) = 1 - P(all questions correct).
Substituting the probability of getting all questions correct, we have:
P(at least one question wrong) = 1 - [tex](1/4)^7[/tex]
Calculating this expression, the probability of getting at least one question wrong is approximately 0.99999, which is essentially equal to 1
Therefore, on a 7-question multiple-choice test with 4 answer choices for each question, the probability of getting at least one question wrong is extremely high, nearly 1. This means that it is highly likely that a test taker will get at least one question wrong on such a test.
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Frank owns a $141,000 home, for which he has a 30-year mortgage in the
amount of $700 a month. Once he has paid off the mortgage, how much will
he have paid in interest?
A. $111,000
B. $120,000
C. $141,000
D. $109,000
Answer: the answer is A !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
After paying off the mortgage, Frank will have accrued interest costs of $111,000 in total. $111,000 is the correct response.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. [tex]A = P(1 + r/n)^{nt[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
The total amount paid by Frank over 30 years will be the product of the monthly payment and the number of months in 30 years:
The total amount paid = Monthly payment × Number of months
Total amount paid = $700/month × 12 months/year × 30 years
Total amount paid = $252,000
However, this total amount includes both the principal (the original loan amount of $141,000) and the interest. To find the amount of interest paid, we need to subtract the principal from the total amount:
Interest paid = Total amount paid - Principal
Interest paid = $252,000 - $141,000
Interest paid = $111,000
Therefore, Frank will have paid $111,000 in interest once he has paid off the mortgage. The answer is A. $111,000.
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I need help please help me asp
New Mexico is the correct option with coordinates (-2.5,-1).
To find the midpoint between two points in the Cartesian plane, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
Here's a step-by-step process to find the midpoint:
1. Identify the coordinates of the two points you want to find the midpoint between. Let's say the coordinates are (x₁, y₁) and (x₂, y₂).
2. Add the x-coordinates of the two points together: x = x₁ + x₂.
3. Divide the sum by 2 to find the x-coordinate of the midpoint: x = x / 2.
4. Add the y-coordinates of the two points together: y = y₁ + y₂.
5. Divide the sum by 2 to find the y-coordinate of the midpoint: y = y / 2.
6. The coordinates (x, y) obtained from steps 3 and 5 represent the midpoint between the two given points.
In the given questions, we need to find the mid-point of Fairfield(-10,1) & Montgomery, Alabama(5,-3).
Let the point be N, N = ((-10 + 5) / 2, (1 + (-3)) / 2).
N = (-2.5,-1)
Therefore, From the given options ,the point where we stop is New Mexico marked at (-2.5,-1).
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Find the variance and standard deviation of the data. Round your answers to the
nearest hundredth.
78, 83, 85, 89, 92, 95
What is the measure of the third angle?
Answer:
90
Step-by-step explanation:
Answer:
90 degrees
Step-by-step explanation:
Step One: In order to solve this problem, you need to know that all angles in a triangle add up to 180 degrees.
Step Two: Now that we know that information, we need to add the angles we do know together: 34+56= 90 degrees.
Step Three: We subtract 90 from 180 to figure out the missing angles: 180-90= 90 degrees.
Preventive medicine services are based on which of the following criteria?
A) Documentation of history, physical examination, and
medical decision making.
B) Age of the patient
C) Amount of time spent with the patient
D) The final diagnosis for the visit
Preventive medicine services are primarily based on documentation of history, physical examination, and medical decision making.
The correct answer is A) Documentation of history, physical examination, and medical decision making. Preventive medicine services focus on preventing or identifying potential health issues before they become more serious. To determine the appropriate preventive measures, healthcare professionals assess various factors. Among these, documentation of the patient's medical history is crucial to understand their individual health risks and needs.
Physical examination allows for a comprehensive assessment of the patient's current health status, identifying any existing conditions or potential areas of concern. Medical decision making refers to the process by which healthcare providers use the gathered information to determine appropriate preventive measures and interventions. Factors like the patient's age, time spent with the patient, and the final diagnosis may be relevant to specific aspects of healthcare but are not the primary criteria for preventive medicine services.
The focus lies on comprehensive documentation and medical decision making to promote and maintain optimal health.
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Find slops ;
3y=9x+18
To find the slope of the line, we need to put the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Divide both sides of the equation by 3 to get y by itself on one side of the equation.
3y = 9x + 18
y = 3x + 6
Step 2: Compare the equation to the slope-intercept form y = mx + b, and we can see that the slope is 3.
Therefore, the slope of the line is 3.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
If function g is a quadratic function that contains the points (-3,5) and (0,14), which statement is true over the interval [-3,0]?
Your answer for this question is B
The average rate of change of f(x) is less than average rate of change of g(x). Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given in the table, then the rate of change of the function f(x) will be
Rate of change of f(x) = (-2 + 4.5) / (-2 + 3)
Rate of change of f(x) = 2.5
If function g is a quadratic function that contains the points (-3,5) and (0,14).
Then the rate of change of the function g(x) will be
Rate of change of g(x) = (14 - 5) / (0 + 3)
Rate of change of g(x) = 9/3
Rate of change of g(x) = 3
Thus, the average rate of change of f(x) is less than average rate of change of g(x).
Then the correct option is C.
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pls pls pls, I beg you to how to put a link I want you to answer this correctly without a link please answer this correctly I beg you
Answer:
1. −51,−41,−38,13,41,50
2. $140 each pair of shoes costs $20 (80 divided by 4). 20 times 7 is 140
3. 5x +6y+1
4. 5+15(n) or using instead of using n for hours use h so, 5+15(h)
5. cylinder
Answer/Step-by-step explanation:
-51, -41, -38, 13, 41, 50
140
5x + 6y + 1
5 + 15h
Cube.
Which of the following would be the FIRST step to take when solving the given equation? -11n - 1 = 87
A) Divide both sides of the equation by 11
B) Subtract 11 from both sides of the equation
C) Subtract 1 both sides of the equation
D) Add 1 to both sides of the equation
Answer:
D) Add 1 to both sides of the equation
Step-by-step explanation:
-11n - 1 = 87
-11n = 87 + 1
i get alot of these please help
Answer:
18 is 3 more than 9- false
18 is 3 times as much as 6 - true
9 is 3 times as much as 27- false
9 is 3 more than 6 - true
A sandwich shop sells sandwiches for $3.50 each, including tax. The shop received a total of $80.50 from the sales of sandwiches one afternoon. Which equation can be used to determine the number of sandwiches, x, sold by the sandwich shop that afternoon? A. 3.50 + x = 80.50 C. 3.50x = 80.50 B. 3.50 + 80.50 = x D. 3.50 ÷ x = 80.50
The number of dandelions at the beginning of the summer was 2,000. The population of dandelions is expected to grow at a rate of 2.5% each day. How many dandelions should we expect after 30 days?
Answer:
3500 dandelions
Step-by-step explanation:
To start you must multiply the number of dandelions by the growth rate to find the number of dandelions grown each day:
2,000 * 0.025 = 50
Then you multiply the number of dandelions by 30 for each day:
50 * 30= 1500
Lastly, you add the dandelions grown in 30 days to the original for your answer.
Identify the measure of the angle indicated.
76
х
The value of 2 that makes lines a and b parallel is
Answer:
x = 76°
Step-by-step explanation:
76° and x are alternative interior angles, so they are congruent when lines a and b are parallel
The population standard deviation for the heights of dogs, in inches, in a city is 3.4 inches. If we want to be 90% confident that the sample mean is within 1 inch of the true population mean, what is the minimum sample size that can be taken?
Answer:
The minimize size that can be taken is - 31.28 or 31 .
Step-by-step explanation:
Lets calculate -
Population standard deviation, [tex]\sigma=3.4 inches[/tex]
Margin of error, E = 1
Critical value , [tex]z_0_._0_5 =1.645[/tex]
Now , the size of the sample , [tex]n=(\frac{z\times \sigma}{E} )^2[/tex]
Putting the given values ,
[tex]=(\frac{1.645\times 3.4}{1})^2[/tex]
= 31.28 or 31 .
The given table of the question has been attached here .
Hence , the answer is 31.
(1/2)x x 3/43=
Pls im so close for finishing 20 POINTS
Answer:
It's 3[tex]x^{2}[/tex]/86
hope this helps:)
Does anyone know the answer so this question
Step-by-step explanation:
f(3)= -2*3^2 +3 -5
= -2*9 +3 -5
= 16
What is the volume of a sphere with a radius of 60.5 ft, rounded to the nearest tenth
of a cubic foot?
Answer:
If rounded to the nearest tenth of a cubic foot, would be: 927587.2
Step-by-step explanation:
The equation of finding the equation of the volume of a sphere is "4π[tex]\frac{radius^{3} }{3}[/tex]"
If values are inserted in for radius as 60.5, the answer will be 927587.2 when rounded to the nearest tenths.
Hope this helps!
HURRY HELP ASAPPP Question 23 of 25
If WXYZ is a square, which statements must be true? Check all that apply.
A. WXYZ is a trapezoid.
B. Wis a right angle.
C. WXYZ is a rhombus.
D. WXXY
E. WXYZ is a rectangle.
OF. WXYZ
WX is perpendicular to XY, W is congruent to X, W is supplementary to X, WXYZ is a rhombus, and WX is parallel to YZ and this can be determined by using the properties of a square.
What is quadrilateral?A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.
Given that, WXYZ is square.
The properties of a square are given below:
All sides are equal in length.
The two consecutive sides are perpendicular.
Opposite sides are parallel to each other.
All the interior angles are 90 degrees.
The diagonals bisect one another.
The area of the square whose sides are 'a' is .
The perimeter of the square whose sides are 'a' is 4a.
Diagonal are equal.
Therefore, the correct statements about the square WXYZ are A), B), C), D), and F).
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