points) A convenience store has two separate locations where customers can be ch

Question

points) A convenience store has two separate locations where customers can be checked out as they leave. These locations each have two cash registers and two employees who check out customers. Let X be the number of cash registers being used at a particular time for location 1 and Y the number being used at the same time at location 2. The joint probability function is given by f(r, y) 12 0 0.12 0.04 0.04 r 1 0.08 0.21 0.06 2 0.05 0.10 0.30 (a) Find E(X) and E(Y). (b) Find Var(X) and Var(Y) (c) Determine E(XY) and correlation pa.y

Explanation / Answer

from above:

joint probability distribution is as follows:

therefore marginal distribtuion of X:

and marginal distribution of Y:

a) hence E(X)=1.25 and E(Y)=1.15

b) Var(X)=0.5875 ; Var(Y)=0.6275

c)E(XY)=1.73

Covaraince =Cov(X,Y)=E(XY)-E(X)*E(Y)=0.2925

therefore correlation coefficient =Cov(X,Y)/((Var(X)*Var(Y))1/2 =0.4817

y x 0 1 2 Total 0 0.1200 0.0400 0.0400 0.2000 1 0.0800 0.2100 0.0600 0.3500 2 0.0500 0.1000 0.3000 0.4500 Total 0.2500 0.3500 0.4000 1.0000

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