CSIR NET Mathematics 2024|Standard distribution | 14 February 2024

Let X be a random variable having probability function

Define , then the distribution of Y is

Let  and  are independent random variables such that

 and . Define

Then which of the following are correct?

If X is a Poisson variate such that  then the mean of X is

If X is standard normal random variable such that  and  then the relation between  and  is

If X is a Poisson random variable with parameter  then the mode of X is