Question
Download Solution PDFFor a random variable X with a variance of 4, the variance of Y = 2X + 7 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- Given, that X is a random variable with a variance of 4. This means Var(X) = 4. And, a random variable Y = 2X + 7, which is a linear transformation of X.
- To find the variance of Y, the most commonly used measure depends on the property that states the variance of a linear transformation.
- According to this property, if Y = aX + b, where X is a random variable and a and b are constants, then the variance of Y is equal to the square of the constant a multiplied by the variance of X.
- In this context, a = 2 and X has a variance of 4.
- Therefore, Var(Y) = (22) × Var(X) = 4 × 4 = 16
Hence, the required variance of Y is 16.
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