Given , where N is a random variable, and Z_i are i.i.d. exponential random variable with rate 1, N and Z_i are independent. What's the relationship between the CDF of X and the CDF of N? Do we have any closed form relations or bounds between them?
Given , where N is a random variable, and Z_i are i.i.d. exponential random variable with rate 1, N and Z_i are independent. What's the relationship between the CDF of X and the CDF of N? Do we have any closed form relations or bounds between them?