GATE 2026 Data Science & AI Q28

Question

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 $t_1$ distribution with probability density function $h(y)$ and cumulative distribution function $H(y)$. Let c be the positive real number for which $g(c) = h(c)$.
Which of the following statements is/are correct?

Accepted Answer

A;C

Answer

$G(0) = H(0)$

Answer

$G(c) < H(c)$

Answer

$G(-c) < H(-c)$

Answer

$g(0) = h(0)$