Homework Answers
Add Answer to:
2. The chi-square distribution plays a significant role in performing inference on the as- sociation between...
proof for distribution of (n-1)S^2/sigma^2 is the chi square distribution with n-1 degrees of freedom. I...
proof for distribution of (n-1)S^2/sigma^2 is the chi square
distribution with n-1 degrees of freedom.
I don't understand the expansion of the square, specifically how
certain terms disappeared and how a sqrt(n) appeared. Also towards
the end, why does V have a degree of freedom of 1? x A detailed
explanation of what happened from step 2 to step 3 would be very
helpful!
THEOREM B The distribution of (n − 1)S2/02 is the chi-square distribution with n – 1...
1. Suppose t hat Xhas t he chi-square distribution on p1∈(0, ∞) degrees of f reedom...
1. Suppose t hat Xhas t he chi-square distribution on p1∈(0, ∞) degrees of f reedom and that, i ndependently, Y has t he chi-square distribution on p2∈(0, p1) degrees of f ree-dom. a. Use moment generating functions to find the distribution of X + Y . b. A naive guess might be that the distribution of X − Y is chi-square on p1− p2 degrees of freedom. Prove that such a guess is wrong by demonstrating that P (X...
#2 2. Let X, N o ?) for i=1,2. Show that Y = X1 + X,...
#2
2. Let X, N o ?) for i=1,2. Show that Y = X1 + X, and Z X; - X2 are independent. 3. Let 2-N(0,1) and W x (n) with Z be independent of W. Show that the distribution of T- tudiatvihustion with n deerees of freedom. (Hint: create a second variable U - find the joint distribution
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and...
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
The following distributional facts apply in this part: All variables are jointly normal and the marginals...
The following distributional facts apply in this part: All variables are jointly normal and the marginals are as follows: N(m,s ): This is the notation for the Normal distribution with mean m and standard deviations . X~N(5,2) Y~N(2,3) Z~N(0,1) W~N(-4,6) U~N(0,5) V~N(24,1) Covariances between these variables are: sxy =.4, sxw =-.5, swu =1, suv =2; allothercovariancesare0. We have a random sample of size 6 from the distribution of X. We have a random sample of size 10 from the distribution...
(a) Let X, have a chi-squared distribution with parameter V, and let X, be independent of...
(a) Let X, have a chi-squared distribution with parameter V, and let X, be independent of X, and have a chi-squared distribution with parameter vz. Show that X, + X, has a chi-squared distribution with parameter v, + V Let Y = X1 + Xy. Identify the correct expression for Fly). Fyly) = (f1 +49 (0) BM={{1*(**) 2*3)**- _jei OFW - 1 -{{49)..:@) ib) dx1 FY) = -xq12 dx + -*2/20 1²ax 2 1/2 O Fy(y) :{"(****): 19). x 22...
A.6.6. We mentioned in class that the Gamma(, 2) distribution when k is a positive integer is cal...
Please answer A.6.6.:
The previous two questions mentioned above are included
below:
A.6.6. We mentioned in class that the Gamma(, 2) distribution when k is a positive integer is called the Chi-square distribution with k degrees of freedom. From the previous two problems, find the mean, variance, and MGF of the Chi-square distribution with k degrees of freedom. A.6.5. In class we showed that if X ~ Gamma(α, β) then E (X) = aß and uar(X) = αβ2 by using...
4. Let 8 >0. Let X, X2,..., X, be a random sample from the distribution with...
4. Let 8 >0. Let X, X2,..., X, be a random sample from the distribution with probability density function S(*;ð) - ma t?e-vor x>0, zero otherwise. Recall: W=vX has Gamma( a -6, 0-ta) distribution. Y=ZVX; = Z W; has a Gamma ( a =6n, = ta) distribution. i=1 E(Xk) - I( 2k+6) 120 ok k>-3. 42 S. A method of moments estimator of 8 is 42.n 8 = h) Suggest a confidence interval for 8 with (1 - 0) 100%...
Having troubles with question 2. Please help 2. If X has a Gamma distribution with parameters...
Having troubles with question 2. Please help
2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...
This is Probability and Statistics in Engineering and Science Please show your work! especially for part B A Poisson distribution with λ=2 X~Pois(2) A binomial distribution with n=10 and π=0.45. X~bin...
This is Probability and Statistics in Engineering and
Science
Please show your work! especially for part B
A Poisson distribution with λ=2 X~Pois(2)
A binomial distribution with n=10 and π=0.45.
X~binom(10,0.45)
Question 4. An inequality developed by Russian mathematician Chebyshev gives the minimum percentage of values in ANY sample that can be found within some number (k21) standard deviations from the mean. Let P be the percentage of values within k standard deviations of the mean value. Chebyshev's inequality states...
proof for distribution of (n-1)S^2/sigma^2 is the chi square
distribution with n-1 degrees of freedom.
I don't understand the expansion of the square, specifically how
certain terms disappeared and how a sqrt(n) appeared. Also towards
the end, why does V have a degree of freedom of 1? x A detailed
explanation of what happened from step 2 to step 3 would be very
helpful!
THEOREM B The distribution of (n − 1)S2/02 is the chi-square distribution with n – 1...
#2
2. Let X, N o ?) for i=1,2. Show that Y = X1 + X, and Z X; - X2 are independent. 3. Let 2-N(0,1) and W x (n) with Z be independent of W. Show that the distribution of T- tudiatvihustion with n deerees of freedom. (Hint: create a second variable U - find the joint distribution
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
(a) Let X, have a chi-squared distribution with parameter V, and let X, be independent of X, and have a chi-squared distribution with parameter vz. Show that X, + X, has a chi-squared distribution with parameter v, + V Let Y = X1 + Xy. Identify the correct expression for Fly). Fyly) = (f1 +49 (0) BM={{1*(**) 2*3)**- _jei OFW - 1 -{{49)..:@) ib) dx1 FY) = -xq12 dx + -*2/20 1²ax 2 1/2 O Fy(y) :{"(****): 19). x 22...
Please answer A.6.6.:
The previous two questions mentioned above are included
below:
A.6.6. We mentioned in class that the Gamma(, 2) distribution when k is a positive integer is called the Chi-square distribution with k degrees of freedom. From the previous two problems, find the mean, variance, and MGF of the Chi-square distribution with k degrees of freedom. A.6.5. In class we showed that if X ~ Gamma(α, β) then E (X) = aß and uar(X) = αβ2 by using...
4. Let 8 >0. Let X, X2,..., X, be a random sample from the distribution with probability density function S(*;ð) - ma t?e-vor x>0, zero otherwise. Recall: W=vX has Gamma( a -6, 0-ta) distribution. Y=ZVX; = Z W; has a Gamma ( a =6n, = ta) distribution. i=1 E(Xk) - I( 2k+6) 120 ok k>-3. 42 S. A method of moments estimator of 8 is 42.n 8 = h) Suggest a confidence interval for 8 with (1 - 0) 100%...
Having troubles with question 2. Please help
2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...
This is Probability and Statistics in Engineering and
Science
Please show your work! especially for part B
A Poisson distribution with λ=2 X~Pois(2)
A binomial distribution with n=10 and π=0.45.
X~binom(10,0.45)
Question 4. An inequality developed by Russian mathematician Chebyshev gives the minimum percentage of values in ANY sample that can be found within some number (k21) standard deviations from the mean. Let P be the percentage of values within k standard deviations of the mean value. Chebyshev's inequality states...
Most questions answered within 3 hours.
-
What does Thomas Whitney imply in his argument regarding
the “Word of God”?
asked 4 minutes ago -
How many mol of Ce4+ are in each 60 μL aliquot of
0.05 M Ce4+?
________...
asked 6 minutes ago -
A nuclear power plant draws 3.0×106 L/min of cooling
water from the ocean.
If the water...
asked 7 minutes ago -
The Civil War cannon Model 1841 has a Muzzle Velocity of
1054ft/s (321.26m/s) if launched at...
asked 12 minutes ago -
C90A3F
What are the four hexadecimal values after the statement
executes and what are the values...
asked 12 minutes ago -
Which of the following is true of clinical significance? A. It
is a measure of how...
asked 44 minutes ago -
Pittsburg Savings & Loan makes four kinds of loans. These
loans, with the yearly interest rate...
asked 28 minutes ago -
a. If your income increases and you are subject to a
proportional tax system, what will...
asked 29 minutes ago -
Healthy people have body temperatures that are normally
distributed with a mean of 98.20 degrees Fahrenheit...
asked 1 hour ago -
1. A crossover study was conducted to investigate whether oat
bran cereal helps to lower serum...
asked 39 minutes ago -
Where are the various locations that viral assembly can occur
within the cell and how does...
asked 38 minutes ago -
Imagine that you are the head of a profitable Silicon Valley
software company seeking to expand...
asked 38 minutes ago