Question 8: Let X and Y be two independent random variables, where X …

Let $X$ and $Y$ be two independent random variables, where $X \sim \mathrm{Normal}(-1, 11)$ and $Y \sim \mathrm{Normal}(1, 9)$. Define $U = 2X - 3Y$. Find the value of $P(U > 2)$. Enter the answer correct to three decimal places.

Hint: Use the following values of $F_Z$ if required. $F_Z$ stands for the CDF of the standard normal.

• $F_Z(0.62) = 0.7343$
• $F_Z(-0.62) = 0.2656$
• $F_Z(1.25) = 0.8947$
• $F_Z(-1.25) = 0.1052$