Skip to content
GATEiit

GATE DA 2026 Q28: Comparing the standard normal and t₁ distributions

Question

Suppose a random variable ZZ follows Normal(μ=0,σ2=1)Normal(\mu = 0, \sigma^2 = 1) distribution with probability density function g(z)g(z) and cumulative distribution function G(z)G(z). Another random variable YY follows t1t_1 distribution with probability density function h(y)h(y) and cumulative distribution function H(y)H(y). Let cc be the positive real number for which g(c)=h(c)g(c) = h(c).

Which of the following statements is/are correct?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
Show answer and explanation

Answer: A, C (official GATE 2026 final answer key)

Concept used: Both densities are symmetric about 0, and t1t_1 (Cauchy) has heavier tails and a lower peak.

First step: By symmetry both CDFs equal 12\tfrac{1}{2} at 0; beyond cc the t1t_1 density is larger, so it puts more mass in the left tail.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

More Probability and Statistics PYQs

PracticePractise Probability and Statistics questions →Full paperAll GATE DA 2026 questions →