Probability and Statistics - Distributions

Suppose a random variable Z follows Normal($\mu$ = 0, $\sigma^2$ = 1) distribution with probability density function $g(z)$ and cumulative distribution function $G(z)$. Another random variable Y follows $t_1$ distributio...

Let X_1,X_2,...,X_n be n independent random variables. Each of the random variables follows Normal(μ = 0, σ² = 1) distribution. Define X̄ = (1/n)Σ_{i=1}^n X_i . Which of the following statements is/are correct?