Question 2: Suppose X has excess distribution over the threshold u of Fu = distribution over...
Question 1 Suppose x, = 1,2,3 has independent N(u,, 1) distributions such that 2, = , = 3u. Let 1 (2g + З23)?; q2 — k(3ӕ, — 2з)?; q 10 91= -G1) Suppose N (u, V); — (х1 х, х3); и 3 (M g and V x (central chi-squared distribution) 2p1 = plz = 3u3 and qa4 ~ (i) Determine whether q, has a chi-squared distribution (ii) Determine the degrees of freedom k and the noncentrality parameter A of q3...
PROB5 Let U and V be independent r.v's such that the p.d.f of U is fu(u) = { 2 OSU< 27, otherwise. and the p.d.f'of2 is Seu, v>0, fv (v otherwise. Let X = V2V cos U and Y = 2V sin U. Show that X and Y are independent standard normal variables N(0,1).
18. suppose that the random variable X has a continuous uniform distribution over [ 10, 20 ]. Find P (15 is less than or equal to X is less than or equal to 19 ) Possible answers : A 0.30, B 0.35, C 0.40, D 0.45
< 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?!
Suppose that Y has pdf given by f(y)=b/(y^2); y>=b, b>0. Suppose also that U has a uniform(0,1) distribution. What must the function g(*) be so that Z=g(U) has the same distribution as Y?
Suppose x has a distribution with u = 25 and o = 20. (a) If a random sample of size n = 50 is drawn, find ui, o j and P(25 sxs 27). (Round Oy to two decimal places and the probability to four decimal places.) My = 25 0x = 2.83 P(25 sxs 27) = x (b) If a random sample of size n = 68 is drawn, find us, o x and P(25 sxs 27). (Round og to...
QUESTION 8 Let V = U ㊥ W where V is a finite-dimensional vector space over a field F, and U and w are subspaces of V. Suppose U1 and U2 are subspaces of U and Wi and W2 are subspaces of W Show that QUESTION 8 Let V = U ㊥ W where V is a finite-dimensional vector space over a field F, and U and w are subspaces of V. Suppose U1 and U2 are subspaces of U...
(4.1) Suppose X is a random variable with normal distribution with u = 2 and o = 2. Compute the following probabilities in terms of the function o (the distribution function of a standard normal distribution). (a) P[O < X < 3). (b) P[X > 2] (c) P[X < 1)
Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0 otherwise Show that the joint density function of U = 3(X-Y) and V = Y is otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (11) te-lul foru R. Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0...
Question No. 6 Suppose that the random variable X has the following uniform distribution: 2 f(x)= 3 ,other wise (18) P(0.33 < X < 0.5) = (A) 0.49 (B) 0.51 (C) 0 (D) 3 (19) P(X> 1.25) = (A) 0 (B) 1 (С) 0.5 (D) 0.33 (20) The variance of X is (A) 0.00926 (B) 0.333 (C) 9 (D) 0.6944