3. A random variable X is said to have a Cauchy(α, β) distribution if and only...
thanks Suppose that Xi and X2 are independent random variables each having PDF: : otherwise (a) Use the transformation technique to find the joint PDF of Yi and Ya where Y-X1 and ½ = Xi +X2. (b) Using your answer to part (a), and the fact that o Vu(1-u) find and identify the distribution of Y2.
5. Suppose that X and X2 are independent random variables each having PDF: each having PDF: : otherwise (a) Use the transformation technique to find the joint PDF of Yi and Yo where Y -X and ½ = Xi +Xg. (b) Using your answer to part (a), and the fact that find and identify the distribution of Y
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...
LetX-Gamma(α = 2, β = 4), Y-Gamma(α = 3, β = 4), X & Y are independent, Z,- , Z,-X + Y. X+Y a) (3 pts) State the joint pdf ofX and Y. Simplify the expression, clearing all Г's. b) (9 pts) Find the joint pdf of Zi and Z2, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression c) (5 pts) You should see...
Let X1 ,……, Xn be a random sample from a Gamma(α,β) distribution, α> 0; β> 0. Show that T = (∑n i=1 Xi, ∏ n i=1 Xi) is complete and sufficient for (α, β).
2. LetX-Gamma(α = 2, β = 4), Y-Gam ma (α = 3, β = 4), X & Y are independent, Z1 = , Z,-X + Y a) (3 pts) State the joint pdf ofX and Y. Simplify the expression, clearing all Г's. b) (9 pts) Find the joint pdf of Zi and Zz, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression (5 pts) You...
10. Let the random variables X ~ NGIX, σ%) and Y ~ Nuy,ơ be jointly continious normal random variables. Now suppose their joint pdf is X and Y are said to have a bivariate normal distribution (a) Given this joint pdf, show that X and Y are independent. (b) The most general form of the pdf for a bivariate normal distribution is What must be true about k for X and Y to be independent bivariate normal random variables? 10....
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
2. LetX~Gamma(α = 2, β = 4), Y~Gamma(α = 3, β = 4), X & Y are independent, Z,-x+r, Z,-X + Y a) (3 pts) State the joint pdf oEX and Y. Simplify the expression, clearing all b) (9pts) Find the joint pdf of Z and Z, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression Z1Z21,2)2048 2048 11 )24e-22/4 c) (5 pts) You should...
Let X and Y be independent exponentially distribution random variables with rate α and β respectively. Find P (X > Y ). Question 13: Let X and Y be independent exponentially distribution random variables with rate a and B respectively. Find P(X> Y).