A value i is said to be the mode of a discrete random

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QUESTION:

A value i is said to be the mode of a discrete random variable X if it maximizes p(x), the probability mass function of X. Find the modes of random variables X and Y with probability mass functions p(x) = *1 2 ,x , x = 1, 2, 3, . . . , and q(y) = 4! y!(4 y)! *1 4 ,y*3 4 ,4y , y = 0, 1, 2, 3, 4, respectively.

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QUESTION:

A value i is said to be the mode of a discrete random variable X if it maximizes p(x), the probability mass function of X. Find the modes of random variables X and Y with probability mass functions p(x) = *1 2 ,x , x = 1, 2, 3, . . . , and q(y) = 4! y!(4 y)! *1 4 ,y*3 4 ,4y , y = 0, 1, 2, 3, 4, respectively.

ANSWER:

Step 1 of 2

The probability mass function of the random variable is

Clearly, is a decreasing geometric sequence with common ratio .

Being a decreasing sequence,

The value of  is which is the maximum and it occurs at .

Therefore, the mode of is .

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