GATE 2020 PI – Question 46

Engineering Mathematics · Probability and Statistics · 2 marks · Numerical answer

A density is f(x)=kx²/2 for −1≤x≤1 and zero elsewhere. Find k.

Show answer and explanation

Correct answer: 3 to 3

Explanation

Normalize the density:1=(k/2)∫₋₁¹x²dx=(k/2)(2/3)=k/3. Hence k=3, which also makes the density nonnegative on its support.

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