Random variables - Gambling and Probability

Two Plus Two Forums Other Topics Probability

Random variables

Post Reply Subscribe

...

10-16-2009 , 05:50 PM

smcdonn2

centurion

Join Date: Jul 2009 Posts: 165

Let Xand Y be independent random variables, each having uniform distribution over the interval (0,1). Let M = maximum(X,Y).

Show that the cdf F_M(x) of M is given by

F_m(x)=x^2 if 0<=x<=1 or 0 otherwise.

What arre the pdf and the expectted value of M?

Quote

10-16-2009 , 06:34 PM

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

lol homework

Quote

10-16-2009 , 08:01 PM

AaronBrown

Pooh-Bah

Join Date: May 2005 Posts: 4,240

F_m(x) is the probability that the maximum of two independent uniform (0,1) variables is less than x. That's the same as the probability that both variables are less than x, which is x^2 for 0<=x<=1. It is 0 for x < 0, and 1 for x > 1 (the problem statement is not correct).

The pdf is the derivative of the cdf, so 2*x from 0 to 1, and 0 outside that range.

The expected value of M is the integral from 0 to 1 of x*2*x = 2*x^2. That integral is 2*x^3/3, which is 2/3 at 1 and 0 at 0, so the expected value is 2/3.

Quote

Post Reply Subscribe

...