Suppose X and Y are independent continuous random variables uniformly distributed on the intervals 0 \leq x \leq 2 and 0 \leq y \leq 4, respectively. Compute the variance of \sqrt{2}X-\frac{1}{2}Y. Hint: First find the variance of X and the variance of Y.

ddaeeric

ddaeeric

Answered question

2021-05-18

Suppose X and Y are independent continuous random variables uniformly distributed on the intervals 0x2 and 0y4, respectively. Compute the variance of 2X12Y. Hint: First find the variance of X and the variance of Y.

Answer & Explanation

Jozlyn

Jozlyn

Skilled2021-05-19Added 85 answers

Step 1
Given information
X and Y independent continuous random variables follows uniform distribution
0x2,0y4
Step 2
Var(X)=(20)212=412=13
Var(Y)=(40)212=1612=43
Variance of ax+by=a2var(x)+b2var(y)
Var(2X12Y)=(2)2Var(X)+(12)2Var(Y)=2×13+14×43=1

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