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__<__X < m + 1

what is pmf of Y?

it's basically asking for P[m

__<__X < m+1]

i know how to solve this for P[m < X

__<__m + 1] ... it would be e

^{-λm}- e

^{-λ(m+1)}because

P[a < X

__<__b] = F

_{x}(b) - F

_{x}(a) and i know the PDF of an exponential random variable. however, in this problem the inequality does not match that so i'm wondering how to solve. i am unsure how to decompose P[m < X

__<__m + 1]. i don't know of any property of the CDF that matches this