GATE 2026 MT – Question 44
Consider a distribution with probability density $$f(x)=\begin{cases}0.5,&0<x<2,\\0,&\text{otherwise}.\end{cases}$$
Given that its mean is 1, the variance is ________. (Rounded off to two decimal places.)
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Correct answer: 0.32 to 0.34
Explanation
Compute $E[X^2]=\int_0^2 0.5x^2\,dx=[x^3/6]_0^2=4/3$. Subtracting the square of the mean gives $\operatorname{Var}(X)=4/3-1^2=1/3$.
To two decimal places, the variance is **0.33**.