2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x <...
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
Homework help with 7.63 please 7.63 Let the random variable X have probability density function f(x)= -π/2 < x <π/2. Find the probability density function of Y sin X by the (a) cumulative distribution function technique, (b) transformation technique. dx1 Hint: The derivative oh-arcsiny is
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
2.6.9 Let X have density function fx(x) = x/4 for 0 < x < 2, otherwise fx(x)=0. (a) Let Y = X. Compute the density function fy(y) for Y. (b) Let Z = X. Compute the density function fz(z) for Z.
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).
4. [10 pts] Let X be a random variable with probability density function if 1 < a < 2, 2 f(a)a 0 otherwise. Find E(log X). Note: Throughout this course, log = loge.
1. Let X and Y have the joint density function given by zob to todos f(x, y) = {kxy) of 50<x< 2, 0 <y<3.) i 279VHb yodmu : 1093 otherwise a) Find the value of k that makes this a probability density function. TO B 250 b) Find the marginal distribution with respect to y. 0x11 sono c) Find E[Y] d) Find V[Y]. X10 sulay boso 50
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...