Question

If a random variable X has a Poisson distribution with mean 5, then the expectation

$E\left[\right(X+2{)}^2]\text{equals}$.

• A. 54

Answer 1

The correct option is A 54

1. case of poisson distribution
   
   Mean = Variance = 5 (given)
   
   $\therefore$ $\text{Variance}\left(x\right)=E\left(x^2\right)-E^2\left(x\right)$
   
   $5=E\left(x^2\right)-(5{)}^2$
   
   $E\left(x^2\right)=30$
   
   So, $E(x+2{)}^2=E[x^2+4x+4)$
   
   $=E\left(x^2\right)+4E\left(x\right)+4$
   
   = 30 + 4 × 5 + 4 = 54