# 6. Let X be a geometric random variable with parameter px 1/2 and let Y be a geometric random variable withparameter 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 help_outlineImage Transcriptionclose6. 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 fullscreen
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Step 1

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

Step 2

The pmf of X is obtained as follows: help_outlineImage TranscriptioncloseР(х -х)- (1-р)" х-1 р х-1 1 1 2 2 -е х-1 1 1 2 1 2 - l2. fullscreen
Step 3

The pmf of Y is obtained as follows:

... help_outlineImage TranscriptioncloseP(Y y) (1-p) р - 3 1 4 4 1 3 4 4 3 4" fullscreen

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