# Thread: Math Stats and Probability proof help

1. ## Math Stats and Probability proof help

Let X ~ Unif(0,1) and Y ~ Unif(0,1) be independent. Let Z = X +Y. Find the pdf for Z and use this to show that Z is NOT Unif(0,2). Thus the sum of two independent uniform random variables is not itself a uniform random variable.

2. ## Re: Math Stats and Probability proof help

density function is correct,

expectation is not,

3. ## Re: Math Stats and Probability proof help

Does E(x)= (a+b)/2, so then would it be (0+2)/2?

4. ## Re: Math Stats and Probability proof help

Originally Posted by ballerninja29
Does E(x)= (a+b)/2, so then would it be (0+2)/2?
$\displaystyle E[X] = \int_{-\infty}^{\infty}~x f_X(x)~dx = \int_0^1~x^2~dx + \int_1^2 x(2-x)~dx$

$E[X] = \left . \dfrac{x^3}{3}\right|_0^1 + \left . x^2-\dfrac{x^3}{3}\right|_1^2= \dfrac 1 3 + 4 - \dfrac 8 3 - 1 + \dfrac 1 3 = \dfrac 1 3 + \dfrac 2 3 = 1$

5. ## Re: Math Stats and Probability proof help

Originally Posted by ballerninja29
Let X ~ Unif(0,1) and Y ~ Unif(0,1) be independent. Let Z = X +Y. Find the pdf for Z and use this to show that Z is NOT Unif(0,2). Thus the sum of two independent uniform random variables is not itself a uniform random variable. Is this the correct answer?
If you want help why do you not post readable questions?