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6. Find the variance of the F distribution for v2> 4, by making use of the...
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
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%...
4. A sample of size n-81 is taken from an exponential distribution with the pdf f(x)-Be-6x, θ > 0, x > 0. The sample mean is i-35. Find a 95% large- sample confidence interval for θ using the Central Limit Theorem.
4. Find the Fisher Information and the Cramer-Rao lower bound for the variance of an unbiased estimator of θ given a random sample . , xn from the density r3 -z/θ where x > 0 and f(x:0-6 94e θ > 0.
Problem 4 (20 points). Show how to use the chi-square distribution to calculate P(a < S2 < b), where S,: nii Σί! from N(μ, σ2) (Xi - X)2 is the sample variance of a random sample Xi,.. . ,Xn
2 3 4 6 . Use the calculator provided to solve the following problems. Suppose that follows a chi-square distribution with 15 degrees of freedom. Compute PG?s19). Round your answer to at least three decimal places. • Suppose again that x? follows a chi-square distribution with 15 degrees of freedom. Find k such that P(x>)0.025. Round your answer to at least two decimal places. . Find the median of the chi-square distribution with 15 degrees of freedom. Round your answer...
11. Bonus problem (6 points) Assume X,...Xm come from a normal population with unknown variance σ' and Y1, Yn come from another normal population with unknown variance and the two samples are independent of each other. Write the 5 steps you will follow to test the hypotheses: Ho-1 Vs Hao #1 Make sure to specify the test statistic and the null distribution (don't forget degrees of freedom), and the rejection region. Hint Remember that-4 ~Xa-1 and-严 (m-1)s2 -X2-1, what do...
QUESTION 5 The statistical results of the test in Question 4 are as follows: F (2, 147)-1.24, p>.05. (1) In the above results, degrees of freedom within or df2 has what value? (2) What is the value of the test statistic? (3) What is the decision about the Null Hypothesis?
imize File Preview ZOOM+ 5. (a) If T has a t-distribution with 9 degrees of freedom, Use Table IV in the book to find tsch that P(T < t) = 0.99 (b) If X has a Chi-Square distribution with 15 degrees of freedom, Use Table V in the 0.95 book to find z such that P(X <z) (c) Suppose a random sample of size 12 is taken from a Normal Population. If the population variance is 8, what is P(S214.3091)....
Use tables to find the area under a Normal Curve! Question 3 3 pts For a standard normal distribution, find the value of zo that satisfies P(z> Zo)- .1038. 1.26 0.26 0.26 0.27