Question

If a random variable X follows a standard normal model N(0, 1), find the

density of X^2

For two independent standard normal random variables X and Y, find

the density of X^2+Y^2

For three independent standard normal random variables X, Y and Z,

find the density of X^2+Y^2+Z^2

If a random variable X follows a normal N(μ,σ^2), and a random variable

Y follows a χ2 (Chi-Square) model with degree of freedom k, assume that X and Y are

independent,

4.1) Use X and Y to construct a t-statistic;

4.2) Derive the density of the t-model that you construct in 4.1).

.PLEASE WRITE IT OUT NEATLY.

Answer 1