GATE 2023 ST – Question 16

Standard Univariate Distributions · Continuous Distributions · 1 mark · Multiple choice

X has density αλ x^(α−1) exp(−λx^α) for x>0,zero otherwise,α,λ>0. Its median is 1 and third quartile is 2. Find (α,λ).

Show answer and explanation

Correct answer: (A) (1,ln 2)

Explanation

The CDF is 1−exp(−λx^α). The median gives exp(−λ)=1/2,so λ=ln 2. At the third quartile exp(−λ2^α)=1/4,so 2^α=2 and α=1. **A**.

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