for a random variable X with parameter λ, Y = m if m < X < m + 1(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Homework Help: PMF of a random varible

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