GATE 2022 BT – Question 55
X has mean 0.1 and variance 0.2. If Y=2X+1, the variance of Y (one decimal place) is ___________.
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Correct answer: 0.79 to 0.81
Explanation
**Rule for variance of a linear function.** For constants $a$ and $b$,
$$\mathrm{Var}(aX+b)=a^2\,\mathrm{Var}(X) .$$
Adding the constant $b$ shifts the distribution but does not change the spread.
$$\mathrm{Var}(Y)=\mathrm{Var}(2X+1)=2^2\times0.2=4\times0.2=\mathbf{0.8}.$$
(The mean 0.1 is not needed.)