A certain market bath X denote the number of penticular timeofdw and let in the

ID: 3223570 • Letter: A

Question

A certain market bath X denote the number of penticular timeofdw and let in the express line at a X2 denote the manter of in the suponespress at the sme time of day. Suppose the joint pdf of Xs and Xa is describod in the following tahie: a. Find the chance there is exaculy one customer in each three less than double b. What is the probability in the superexpress the number of paop the espress lane of Xu d How many people are espected to be in the express hine ar Exil' e. By inspection the probabilities PX 4A PDK1-0, and PXi 4, Xa"0M are Xs and Xs independent random variables? Explain.

Explanation / Answer

Part-a

P(X1=1, X2=1)=0.10

Part-b

P(X2=2X1-3) = P(2X1-X2=3)

=P(X1=2,X2=1)+P(X1=3,X=3)

=0.07+0.03

=0.10

Part-c

Marginal pdf of X2 is as follows:

f(x2)

0.05+0.15+0.05+0+0

=0.25

0.20+0.10+0.07+0.03+0

=0.40

0+0.03+0.10+0.04+0.03

=0.20

0+0.00.03+0.03+0.07

=0.15

Part-d

E(x1)=0*0.25+1*0.30+2*0.25+3*0.10+4*0.10=1.5

Part-e

P(X1=4)=0.10

P(X2=0)=0.25

P(X1=4,X2=0)=0

As P(X1=4,X2=0) P(X1=4)* P(X2=0)

So, X1 and X2 are not independent.