Question

The citizens of Montana withdraw money from a cash machine according to the following probability function (X): 102 0,28 The number of customers per day has poisson distribution with 2-816 Amount(S) P(X-x) 132 0,5 184 0,22 Calculate the expected money withdrawn for a given day Calculate the A) Cov(X,Y) B)Corr(X,Y) according to Item 10

Answer 1

Amount of money withdrawn a customer = X

Number of customers per day = Y (let)

$\therefore$ Amount of money withdrawn for a given day = XY

A customer withdraws money independent of number of customers per day: i.e X and Y are independent.

$\therefore$ E(XY) = E(X) $\times$ E(Y)

E(X) = $102 $\times$ 0.28 + $132 $\times$ 0.5 + $184 $\times$ 0.22 = $135.04

Y ~ Poi( $\lambda$ ) $\Rightarrow$ E(Y) = $\lambda$ = 816

$\therefore$ E(XY) = E(X) $\times$ E(Y) = $135.04 $\times$ 816 = $110192.64

A) X and Y are independent $\Rightarrow$ Cov(X,Y) = 0

B) Cov(X,Y) $\Rightarrow$ Corr(X,Y) = 0