GATE 2025 CE (CE2) – Question 51
Consider a discrete random variable $X$ whose probabilities are given below. The standard deviation of the random variable is ______ (round off to one decimal place).
| $x_i$ | 1 | 2 | 4 | 8 |
|---|---|---|---|---|
| $P(X = x_i)$ | 0.3 | 0.1 | 0.3 | 0.3 |
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Show answer and explanation
Correct answer: 2.79 to 2.81
Explanation
The mean is $E[X] = 0.3 + 0.2 + 1.2 + 2.4 = 4.1$. The mean of the squares is $E[X^2] = 0.3 + 0.4 + 4.8 + 19.2 = 24.7$. The variance is $24.7 - 4.1^2 = 7.89$ and the standard deviation is $\sqrt{7.89} = 2.81 \approx 2.8$.