Question

Consider two random variable X and Y with joint PMF given in the table below. Y...

Consider two random variable X and Y with joint PMF given in the table below.

Y = 2 Y = 4 Y = 5
X = 1 k/3 k/6 k/6
X = 2 2k/3 k/3 k/2
X = 3 k k/2 k/3

a) Find the value of k so that this is a valid PMF. Show your work.

b) Re-write the table with the joint probabilities using the value of k that you found in (a).

c) Find the marginal PMFs of X and Y. Show your work.

d) Find P(X ≤ 2, Y ≤ 4)

e) Find P(Y=2 | X=1). Show your work.

f) Are X and Y independent? Justify with calculations.

Math   Statistics-And-Probability   
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Answer #1

check the calculations and study the joint distribution function for discrete random variable. If you have any doubt you can ask me.

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