Suppose that a random variable $Y$ has a probability density function given by $$ f(y)=\left\{\begin{array}{ll} ky^3e^{-y/2}, & y>0\\ 0, & \textrm{elsewhere} \end{array} ight. $$ (a). Find the value of {\color{red}168}$ that makes $f(y)$ a probability density function. (b). Does $Y$ follow a $\chi^2$ distribution? If so, how many degrees of freedom? (c). What are the mean and standard deviation of $Y$?

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