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(a) Display the joint pmf of

`x`

and

`Y`

in a joint probability table. (b) Compute and

`Y<=1`

by adding probabilities from the joint pmf, and verify that this equals the product of

`P(x<=1)`

and

`P(Y<=1)`

. (c) Express the event that the total number of beds occupied at the two hospitals combined is at most 1 in terms of

`x`

and

`Y`

.

`{x,Y:x*Y<=1}`

`{x,Y:x+Y<=1}`

`{x,Y:x-Y>=1}`

`{x,Y:x+Y>=1}`

`{x,Y:x-Y<=1}`

Calculate this probability. (d) What is the probability that at least one of the two hospitals has no beds occupied?