easy Probability
A release-checked easy problem for training Continuous Random Variables, Limit Theorems.
Let $X_1,\dots,X_{324},Y_1,\dots,Y_{324} \sim \text{Beta}(1,2)$ IID. Define $S_{324} = X_1 + \dots + X_{324}$ and $T_{324} = Y_1 + \dots + Y_{324}$. Approximate $\mathbb{P}[S_{324} - T_{324} > 10]$. Your answer should be in the form $\Phi(a)$, where $\Phi$ is the standard normal CDF. Find $a$.
This Probability problem is tagged Continuous Random Variables, Limit Theorems. 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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