Allied & ICAR Exam Bank • ALLIED_0088 NAT • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Mean, median, mode and standard deviation

Question Statement:

The variance of a discrete random variable that takes value $2$ with probability $0.5$ and value $4$ with probability $0.5$ is:

Answer Key:

1

Step-by-Step Solution & Explanation

Mean $\mu = 2(0.5) + 4(0.5) = 3$. Variance $E[(X-\mu)^2] = (2-3)^2(0.5) + (4-3)^2(0.5) = 1(0.5) + 1(0.5) = 1.0$.
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