Homework SourseConsider three independent random variables P Q and R such t
Consider three independent random variables P, Q, and R such that E[P] = 3, Var(P) = 2, E[Q] = 2, Var(Q) = 1, and E[R] = 1, Var(R) = 3 respectively. Define a new random variable S by S = -P + 3Q -2R.
(a) Find the mean and variance of S.
(b) If P, Q, and R are normally distributed, what\'s the distribution of S? Compute P(S>9).
**Please show work**
Solution
![Consider three independent random variables P, Q, and R such that E[P] = 3, Var(P) = 2, E[Q] = 2, Var(Q) = 1, and E[R] = 1, Var(R) = 3 respectively. Define a ne](/WebImages/8/consider-three-independent-random-variables-p-q-and-r-such-t-997128-1761513279-0.webp "Consider three independent random variables P, Q, and R such that E[P] = 3, Var(P) = 2, E[Q] = 2, Var(Q) = 1, and E[R] = 1, Var(R) = 3 respectively. Define a ne")
