Finding cdf and pdf of variable.

[cookiesyum]

Homework Statement

Let X1 X2 X3 and X4 be four independent random variables, each with pdf f(x) = 3(1-x)², 0<x<1, zero elsewhere. If Y is the minimum of these four variables, find the cdf and pdf of Y.

The Attempt at a Solution

P(Y<or= y)

= 1 - P(Y>y)
= 1 - P(X1>y, X2>y, X3>y, X4>y)
= 1 - P(X1>y)P(X2>y)P(X3>y)P(X4>y)
= 1 - [3(1-x)²]⁴

which does NOT equal (1-y)¹², which is the answer in the back of the book. Don't know where I'm going wrong...

 

[clamtrox]

What is P(x_1 > y)? It's certainly not that. Maybe you should try integrating over f instead.

 

[cookiesyum]

What is P(x_1 > y)? It's certainly not that. Maybe you should try integrating over f instead.

Got it! Thanks so much for the help.