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. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.06 0.20 0.07 2 0.05 0.14 0.33 (a) What is P(X

Answer 1

`P(x = 1) = 0.33`

`P(y = 2) = 0.42`

Explanation:

Given

y

x
`\begin{array}{cccc}P(x,y) & {0} & {1} & {2} & {0} & {0.10} & {0.03} & {0.02} & {1} & {0.06} & {0.20} & {0.07} & {2} & {0.05} & {0.14} & {0.33}\ \end{array}`

Solving (a)

`P(x = 1)`

To do this, we simply add all data where x = 1

So, we have:

`P(x = 1) = P(x=1|y=0) + P(x=1|y=1) + P(x=1|y=2)`

`P(x = 1) = 0.06 + 0.20 + 0.07`

`P(x = 1) = 0.33`

Solving (b)

`P(y = 2)`

To do this, we simply add all data where y = 2

So, we have:

`P(y = 2) = P(x=0|y=2) + P(x=1|y=2) + P(x=2|y=2)`

`P(y = 2) = 0.02 + 0.07 + 0.33`

`P(y = 2) = 0.42`