A.) Let f(x) = 2/4x for x =1,2,..., and f(x) = 0 otherwise. Is f a probability d

Question

A.) Let f(x) = 2/4x for x =1,2,..., and f(x) = 0 otherwise. Is f a probability density function?

B.) Let F(x) = (x-1)/x for for x 1, and f(x) = 0 otherwise. If F a cumulative distribution function?

C.) Let F(x) = (x+1)/x for for x 1, and f(x) = 0 otherwise. If F a cumulative distribution function?

D.) Let F(x) = (x-1)/(2x) for for x 1, and f(x) = 0 otherwise. If F a cumulative distribution function?

The answers are as followed: A. No, B. Yes, C. No, D. No

But i dont understand how to figure that out. Please help

Explanation / Answer

to dind if is a probability density function we need to find the intergral of the function between the number that the variable can take

for example for the first literal we need to do an integral from 1 to infinite and see if the value is 1, if the value is not one we say that f is not a probability density function

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