Final answer:
The variance of the expression 3X - 4Y, where X and Y are independent random variables with variances 2 and 3 respectively, is calculated using the variance formula for a linear combination of independent variables and is determined to be 66. Therefore correct option is E
Step-by-step explanation:
The variance of a linear combination of independent random variables can be found using the formula
Var(aX + bY) = a²Var(X) + b²Var(Y), where a and b are constants and X and Y are the random variables.
Given that Var(X) = 2 and Var(Y) = 3, for the combined variable 3X - 4Y, we calculate the variance as follows:
- For X, multiply its variance by the square of its coefficient: (3)² * 2 = 9 * 2 = 18.
- For Y, multiply its variance by the square of its coefficient: (-4)² * 3 = 16 * 3 = 48.
- Add the results to get the variance of 3X - 4Y: 18 + 48 = 66.
Therefore, the variance of 3X - 4Y is 66.
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If x and y are two independent random variables with variances 2 and 3, find the variance of 3x - 4y.
A. 25
B. 26
C. 19
D. 16
E. 66