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A value i is said to be the mode of a discrete random
Chapter , Problem 6(choose chapter or problem)
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 .