Question: Please indicate whether the following statements are true \((\mathrm{T})\) or false \((\mathrm{F})\).

1. \(\mathrm{T} / \mathrm{F}\). For any two random variables \(X\) and \(Y\), if \(\operatorname{Cov}(X, Y)=0, X \perp Y\).
2. \(\mathrm{T} / \mathrm{F}\). For any events \(A\) and \(B, P(A \cap B)=P(A) P(B)\).
3. \(\mathrm{T} / \mathrm{F}\). If \(X\) is a normally distributed random variable, any linear
   transformation of \(X\) will also be normally distributed.
4. \(\mathrm{T} / \mathrm{F}\). Events that are mutually exclusive are independent.
5. \(\mathrm{T} / \mathrm{F}\). The cdf is the area under the curve to the left of a point in the pdf.

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