- #1
magnifik
- 360
- 0
for a random variable X with parameter λ, Y = m if m < 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] = Fx(b) - Fx(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
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] = Fx(b) - Fx(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