Question

the table below shows the probability distrubution of a random variable y y - -2 ,-1, 0,1,2,3,4 P(Y) 0.02,0.06,0.19,0.14,0.53,0.04,0.02What is the expected value of Y

Answer 1

The expected value is given by:

`E(Y)=\sum ^n_(i\mathop=0)y_iP(y_i)`

Therefore:

`\begin{gathered} E(Y)=(-2\cdot0.02)+(-1\cdot0.06)+(0\cdot0.19)+(1\cdot0.14)+\ldots+ \\ +\cdots+(2\cdot0.53)+(3\cdot0.04)+(4\cdot0.02) \\ E(Y)=1.3 \end{gathered}`