3. V, W, X and Y are independent random variables, each having a normal distribution. V has mean 4 and variance 5. W has mean -2 and variance 4. X has mean 5 and variance 3. Y has mean -4 and variance 4. Find Prob(V+ W>X+ Y). (Hint: Consider first the random variables R = V+ W and U=X+ Y. Then consider the random variable D= R - U.) [8]

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3. V, W, X and Y are independent random variables, each having a normal distribution. V has
mean 4 and variance 5. W has mean -2 and variance 4. X has mean 5 and variance 3. Y has mean
-4 and variance 4. Find Prob(V+ W>X+ Y). (Hint: Consider first the random variables
R=V+ W and U=X+Y. Then consider the random variable D= R - U.)
[8]
Transcribed Image Text:3. V, W, X and Y are independent random variables, each having a normal distribution. V has mean 4 and variance 5. W has mean -2 and variance 4. X has mean 5 and variance 3. Y has mean -4 and variance 4. Find Prob(V+ W>X+ Y). (Hint: Consider first the random variables R=V+ W and U=X+Y. Then consider the random variable D= R - U.) [8]
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