A service station has both self-service and full-service islands. On each island

Question

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) y

0 1 2

0 .1 .04 .01

x 1 .06 .2 .06

2 .06 .14 .33

(a) What is P(X = 1 and Y = 1)?
P(X = 1 and Y = 1)

(b) Compute P(X 1 and Y 1).
P(X 1 and Y 1)

Compute the probability of this event.
P(X 0 and Y 0) =

(d) Compute the marginal pmf of X.

Compute the marginal pmf of Y.

Using pX(x), what is P(X 1)?
P(X 1) =

Explanation / Answer

a)

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

b)

P(X<=1 and Y<=1)

= 0.1 +0.04 + 0.06 + 0.2

= 0.4

c)

P(X !=0 and Y !=0)

= 1 - P(X=0 and Y=0)

= 1 - 0.1

= 0.9

d)

pX(0) = 0.1 +0.04 + 0.01 = 0.15

pX(1) = 0.06 + 0.2 + 0.06 = 0.32

pX(2) = 0.06 + 0.14 + 0.33 = 0.53

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