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).
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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.
Oh hello professor. It is the same answer he gave me. It is on your book.
Originally Posted by lera Oh hello professor. It is the same answer he gave me. It is on your book. hint $X \sim N\left(\mu_x, \sigma_x\right)$ $Y \sim N\left(\mu_y,\sigma_y\right)$ $X+Y \sim N\left(\mu_x + \mu_y,~\sqrt{\sigma_x^2+\sigma_y^2}\right)$