Expectation of Discrete Random Variables?

Question

For the next 3 questions:

X is a random variable with μx = 8.7 and σx = 18.5
Y is a random variable with μy = 14.9 and σy = 21.0
X and Y are independent.

1. What is the mean of X + Y?
2. What is the standard deviation of X + Y?
3. What is the standard deviation of X - Y?

1. E(X + Y) = E(X) + E(Y) = 8.7 + 14.9 = 23.6
23.6 / 2 = 11.8

2. Var (X + Y) = Var (X) + Var (Y) -> COV = 0 since independant
= 18.5^2 + 21.0^2 = 342.25 + 441 = 783.25

SD = Sqrt(783.25) = 27.99

3. I get a negative number following the same steps I used above, and obviously you can't square root a negative number. Am I doing something wrong?

Anyways, am I doing these questions properly? Any help or suggestions would be AWESOME.

Anonymous · Answer

think of 40 rolls of a 1p. On widespread, what proportion wins? How lots did you %. up? On widespread,what proportion losses? How lots did the stall proprietor %. up? So on the top of 40 rolls, what proportion 1p funds are you preserving? (could be a minus sort!) Divide via 40 on your expectation on a million roll. Repeat for the 2p coin.

fcas80 · Answer

1. E(X + Y) = E(X) + E(Y) = 8.7 + 14.9 = 23.6

2. is correct.

3. SD of (X-Y) = SD of (X+Y)

georgie b · Answer

3) Var(a X) = a^2 Var(X)
Therefore : Var(X - Y) = Var(X) + Var(Y)

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Expectation of Discrete Random Variables?

3 Answers