6、(12%) A random variable Y follows Uniform(-1,3). Derive the probability density function of W = Y^2.

8. (14%) P represents the probability of adverse reaction not happening for a vaccination. P is a random variable with density functions: $$\left\{ \begin{array}{ll} 12p^2(1-p) & 0 \le p \le 1 \\ 0 & otherwise \end{array} \right.$$ Let n be the number of persons who have been injected. Y is the number of persons that adverse reaction does not happen after vaccination. Please calculate E(Y) if n=10.

6、(12%) A random variable Y follows Uniform(-1,3). Derive the probability density function of \( \mathrm{W} = \mathrm{Y}^2 \).

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