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Asked Dec 3, 2019
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6

6. Let X be a geometric random variable with parameter px 1/2 and let Y be a geometric random variable with
parameter py 3/4. If X and Y are independent,
(a) Determine the joint pmf of X and Y and then
(b) Find the probability that X Y 2
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6. Let X be a geometric random variable with parameter px 1/2 and let Y be a geometric random variable with parameter py 3/4. If X and Y are independent, (a) Determine the joint pmf of X and Y and then (b) Find the probability that X Y 2

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Expert Answer

Step 1

It is given that the variables X and Y are independent.

Step 2

The pmf of X is obtained as follows:

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Р(х -х)- (1-р)" х-1 р х-1 1 1 2 2 -е х-1 1 1 2 1 2 - l2.

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Step 3

The pmf of Y is obtained as follows:

...
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P(Y y) (1-p) р - 3 1 4 4 1 3 4 4 3 4"

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