Question
We have $X \sim N(0,1)$ and $Y \sim N(0,4)$ are independent. Compute $\mathbb{E}[|Y - X|]$. The answer will be in the form $\left(\dfrac{K}{\pi}\right)^b$ for rational $b$ and $K$. Find $bK$.
medium Probability
Absolute Normal Difference
A release-checked medium problem for training Expected Value, Continuous Random Variables, Calculus.
Practice focus
This Probability problem is tagged Expected Value, Continuous Random Variables, Calculus. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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