# Thread: I need help pls (Random Variables)

1. ## I need help pls (Random Variables)

Let X and Y be independent random variables with PDFs N83,9) and N(5,7) respectively. Consider a new random variable Z=X+Y. Find P(Z≤0).

2. ## Re: I need help pls (Random Variables)

You should know the distribution of the sum of two normal variates, or at least be able to look it up in your book.

Find that distribution and apply it.

3. ## Re: I need help pls (Random Variables)

Oh hello professor. It is the same answer he gave me. It is on your book.

4. ## Re: I need help pls (Random Variables)

Originally Posted by lera
Oh hello professor. It is the same answer he gave me. It is on your book.
hint

$X \sim N\left(\mu_x, \sigma_x\right)$

$Y \sim N\left(\mu_y,\sigma_y\right)$

$X+Y \sim N\left(\mu_x + \mu_y,~\sqrt{\sigma_x^2+\sigma_y^2}\right)$