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Safari File Edit View History Bookmarks Window Help . C O *_ 48960 Mon 5:08 PM Allis Adimey a webassign.net EXAM 02 Chegg Study | Guided Solutions and Study Help | Chegg.com Given we do not know the true population mean, it is possible to A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation p(x, y) 0 0.10 0.05 0.02 1 0.07 0.20 0.07 2 0.05 0.14 0.30 (a) what is P(X = 1 and Y = 1)? P(X 1 and Y = 1) = (b) Compute P(X 1 and Y š1) P(X |and Y 1) = (c) Given 2 hoses are being used on the self-service island, what is the probability at least 1 hose is being used at the full-service island? (Use 5 significant digits)- Compute the probability of this event, P(X 0 and Y 0) = (d) Compute the marginal pmf of X Px(x) Compute the Expected number of hoses being used on the self-service island Compute the marginal pmf of Y 0 6

Explanation / Answer

a) P(X=1 and Y=1)=0.2

b)P(X<=1 and Y<=1)=P(X=0,Y=0)+P(X=0,Y=1)+P(X=1,Y=0)+P(X=1,Y=1)=0.1+0.07+0.05+0.2 =0.42

c)

P(Y>=1|X=2) =(0.14+0.3)/(0.05+0.14+0.3)=0.8980

probability P(X not 0 and Y not 0) =1-P(X=0,Y=0)=1-0.1 =0.9

d)

marginal pmf of x:

expected value of X =E(X)=1.32

marginal pmf of Y:

E(Y) =1.17

Cov(X,Y)= E(XY)-E(X)*E(Y) =0.2756

Correlation =Cov(X,Y)/(Var(X)*Var(Y))1/2 =0.4842

e)

option A is correct not independent because p(x,y) is not equal to p(x)*p(y)

x 0 1 2 P(x) 0.17 0.3400 0.49

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