Question: A discrete random variable (Y) has discrete distribution given in the following table: (a) Calculate (P(0 (b) Calculate (mathrm{E}[Y]). (c) Calculate (operatorname{Var}[Y]). (begin{array}{ll}text { (d)

A discrete random variable $Y$ has discrete distribution given in the following table:

Yi f(yi) .1 0 1 2 23 .2 .3 5 .4

(a) Calculate $P(0
(b) Calculate \(\mathrm{E}[Y]$.
(c) Calculate $\operatorname{Var}[Y]$.
$\begin{array}{ll}\text { (d) Let } W=3 Y & \text { 1. Calculate } \mathrm{E}[W] \text {. }\end{array}$
(e) Calculate $\operatorname{Var}[W]$.

Yi f(yi) .1 0 1 2 23 .2 .3 5 .4

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