10) Suppose that X follows a chi-square distribution with m degrees of freedom and S=X+Y. Given...
Suppose that χ2 follows a chi-square distribution with 20 degrees of freedom. Compute P (χ2 ≤ 24). Round your answer to at least three decimal places. Suppose again that χ2 follows a chi-square distribution with 20 degrees of freedom. Find k such that P(χ2 >k) = 0.1. Round your answer to at least two decimal places. Find the median of the chi-square distribution with 20 degrees of freedom. Round your answer to at least two decimal places.
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...
3. If a random variable Y has a Chi-square distribution with 9 degrees of freedom. a) The mean of the distribution is b) The standard deviation of the distribution is c) The probability, p( y = 5) = d) The probability, P(Y>8 ) = e) the probability, p( y < 2) = _
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...
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...
The Chi-Square Table (Chapter 17) The chi-square table: The degrees of freedom for a given test are listed in the column to the far left; the level of significance is listed in the top row to the right. These are the only two values you need to find the critical values for a chi-square test. Increasing k and a in the chi-square table Record the critical values for a chi-square test, given the following values for k at each level...
Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, respectively. (a) Show that Yı = X1/X2 and ½ = X1 + X2 are independent and that ½ is x 2) (b) Deduce that and KJr2 (X1+X2)/(n+r2) are independent F-variables. 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, respectively. (a) Show that Yı = X1/X2 and ½ =...
00 Use the calculator provided to solve the following problems. • Suppose that y follows a chi-square distribution with 8 degrees of freedom. Compute P(Asy's 12). Round your answer to at least three decimal places. • Suppose again that y follows a chi-square distribution with 8 degrees of freedom. Find k such that PG?Zk) -0.025. Round your answer to at least two decimal places • Find the median of the chi-square distribution with 8 degrees of freedom. Round your answer...
9. Show that Y-Σ|-1 z? has a Chi-squared distribution with n degrees of freedom, where Z's are iid rvs from a standard normal distribution. (Prove it mathematically)
Let Yn be a chi square random variable with n degrees of freedom, and let Xn = Yn / n2. Find the limiting distribution of Xn.