1 answer

The citizens of Montana withdraw money from a cash machine according to the following probability function...

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of customers per day has poisson distribution with 2-816 Amount(S) P(X-x) 132 0,5 184 0,22 Calculate the expected money withdrawn for a given day Calculate the A) Cov(X,Y) B)Corr(X,Y) according to Item 10
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of customers per day has poisson distribution with 2-816 Amount(S) P(X-x) 132 0,5 184 0,22 Calculate the expected money withdrawn for a given day Calculate the A) Cov(X,Y) B)Corr(X,Y) according to Item 10

Answers

Amount of money withdrawn a customer = X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\therefore Amount of money withdrawn for a given day = XY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\times0.28 + $132\times0.5 + $184\times0.22 = $135.04

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

\therefore E(XY) = E(X) \times E(Y) = $135.04\times816 = $110192.64

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

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

.

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