Question 1 Suppose x, = 1,2,3 has independent N(u,, 1) distributions such that 2, = ,...
Practice problems using various statistical methods If n independent random variables X have normal distributions with means μ and the standard deviations σ , then determine the distribution of a. I. X-E(X) var(X) C. 2. If n independent random variables Xi have normal distributions with means μί and the standard deviations σί, then determine the distribution of a. b. Y -a1X1 + a2X2+ + anXn (ai constant) X-E(X) Vvar(X) 3. What is CLT? Proof briefly? What are t-, Chi-squared- and...
Let XinGamma (A, 1) are independent fort = 1, 2, , n. Define X.Hi for i = 1,2,3, , n-1 and Yn-Σ"키 X. Find the joint and marginal distributions of Let XinGamma (A, 1) are independent fort = 1, 2, , n. Define X.Hi for i = 1,2,3, , n-1 and Yn-Σ"키 X. Find the joint and marginal distributions of
Suppose X, Y are independent with X ∼ N (0, 1) and Y ∼ N (0, 1). Show that the distribution of Q = X/Y follows the Cauchy distribution, i.e., f(q) = 1/π(1+q2) . Hint: Let Q = X/Y and V=Y. Find the joint pdf of Q and V and finally find the marginal pdf of Q by integrating the joint pdf of Q and V w.r.t. V: Y π(1+q2) Y V = Y . Find the joint pdf of...
Question 2: Suppose X has excess distribution over the threshold u of Fu = distribution over the threshold v is equal to F, = G.+(-u) for v u.
Please explain if any of my answers are wrong. Thank you. Suppose a statistician wishes to test whether a large number of observations Xi follows an exponential distribution with parameter A = 1. He wishes to test this hypothesis exactly, and intends that if the observations follow an exponential distribution with a different parameter the test should reject the null hypothesis given sufficiently many observations. In addition, he wants to have a numeric statistic that he could report and does...
1. Let X be an iid sample of size n from a continuous distribution with mean /i, variance a2 and such that Xi e [0, 1] for all i e {1,...,n}. Let X = average. For a E (0,1), we wish to obtain a number q > 0 such that: (1/n) Xi be the sample Р(X € |и — 9. и + q) predict with probability approximately In other words, we wish to sample of size n, the average X...
Suppose an x distribution has mean μ = 2. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81. (a) What is the value of the mean of each of the two x distributions? For n = 49, μ x = For n = 81, μ x = (b) For which x distribution is P( x > 2.5) smaller? Explain your answer. The distribution...
< 0) = 1/3, and Exercise 9.8. Suppose X has an N(u,02) distribution, P(X P(X < 1) = 2/3. What are the values of u and o?!
Answer all parts please. Question 3: Suppose that X and Y are i.i.d. N(0,1) r.v.'s (a) (5 marks). Find the joint pdf for U Х+Ү andV — X+2Y. (b) (3 marks). The joint pdf of U and V is for what particular distribution? (Hint: See p.81 of the textbook.) (c) (2 marks). Are U and V independent? Why?
2 (25 pts). Let an algorithm has complexity S(n)=S(n-1)+f(n), where for k=1,2,3,... f(k)=k+k/3. Answer these two questions: (1) Find the closed form for S(n) if S(2)=1. (2) Prove by mathematical induction that the closed form you found is correct.