Problem 4. The median of a PDF fx(x) is defined as the number a for which...
5.1 Let fx(x) be given as fx(x) = Ke-x"Au(x), where A = (1, ..., I T with li > O for all i, x = (21,...,27), u(x) = 1 if r;>0, i=1,...,n, and zero otherwise, and K is a constant to be determined. What value of K will enable fx(x) to be a pdf? diena - co ma wana internetow
1 x Suppose X has an exponential distribution, thus its pdf is given by fx (x) = 5e8,0 5x<0, 2> 0;0 0.w. a. Find E(X) b. Find E(X(X-1) c. Find Var (x)
Problem 1 The pdf of X, the lifetime of a certain type of electronic device in hours, is given by if x > 10 10 if x < 10 f(x) = { ift 1. (1 point) Find the constant c that makes the a valid pdf. 2. (1 point) Find P(X > 20) 3. (1 point) Find F(x), i.e. the cummulative distribution of X? 4. (1 point) What is the median value of X?
3. Suppose that X has pdf fx(x) = 3, x > 1 and Y has pdf 24» fy(y) = ¡2, x 〉 1. Suppose further that X and Y are inde- pendent. Calculate the P(X 〈 Y).
3. Let X has the following pdf: {. -1 <1 fx(a) otherwise 1. Find the pdf of U X2. 2. Find the pdf of W X
The random Variable X has a pdf fx (2) = {*** kr + > -1 <r<2 otherwise Y is a function of X and is derived using Y = g(x) = X S -X X2 X <0 X>0 Find: (A) fr(y) (B) E[Y] using fy(y) (C) EY] using fx (2)
Fx(x) L - - +--- - + -2 -1 1 2 CDF Ex(x) Let X have CDF Fx(2) shown in a) Find P[X > 0.5] and P[X > 1). b) Find E[X].
8) Assume that X ~ N(μ = 4,02-1). Find c >0 such that P(-c 〈 X 〈 c) Find P(2 〈 X 〈 6) a. 0.95 b.
pectively, 3. Ajoint pdf is defined by (C(x + 2y), for 0 <x< 2, and 0 < y< 1, fx.r(x,y) = -{-4** 0. otherwise. a. Find the value of C. b. Find the marginal pdf of X alone. 9 c. Find the pdf of U = U = x+132 4. Consider n independent rvs XX2, ..., X, having the same distribution with a common variance a?. For any i = 1,2, ..., n, find Cov(x,- 8, 8), where 8 =...
NIS 4) The joint pdf of X and Y is 1, 0<x<1, 0<y< 2x, fx,8(8,y) = { 0, otherwise. otherwise. or 1 (Note: This pdf is positive (having the value 1) on a triangular region in the first quadrant having area 1.) Give the cdf of V = min{X, Y}. x