1.If X is a Gaussian random variable with zero mean and variance equal to 1, then the density
function of Z = is equal to 2fx(z), z ≥ 0.
2. The sum of a random number of independent Gaussian random variables with zero mean and unit variance results in a Gaussian random variable regardless of the distribution of N (the number of variables in the sum).
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Are these statements true or false & explain why?
It is true,
To get the pdf of Z, we need to find the distribution of Z first.
Gaussian Random Variables are investigated. The solution is detailed and well presented.