GATE 2023 IN – Question 32
A discrete random variable $X$ takes values 0, 1, 2, with $P(X=0)=0.25$ and $P(X=1)=0.5$. If $E[\cdot]$ denotes expectation, $E[X]-E[X^2]$ is ______ (one decimal place).
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Show answer and explanation
Correct answer: -0.5 to -0.5
Explanation
The remaining probability is $P(X=2)=0.25$.
Thus $E[X]=0.5+2(0.25)=1$ and $E[X^2]=0.5+4(0.25)=1.5$. Their difference is **−0.5**.