4)
p = 1 - (0.3 + 0.1 + 0.4) = 0.2
Distribution of X2 is
P(X2 = 4) = 0.3 + 0.4 = 0.7
P(X2 = 0) = 0.1
P(X2 = 1) = 0.2
So, P(X2 2) = 0.7
E(X) = -2 * 0.3 + 0 * 0.1 + 1 * 0.2 + 2 * 0.4 = 0.4
5)
E[X] = 10 * 0.4 = 4
Var[X] = 10 * 0.4 * (1-0.4) = 2.4
E(Y) = E(2X + 5) = 2E(X) + 5 = 2 * 4 + 5 = 13
Var(Y) = Var(2X + 5) = 22Var(X) + 0 = 4 * 2.4 = 9.6
6)
If X and Y are independent,
Var(X - 2Y) = Var(X) + (-2)2 Var(Y) = 4 + 4 * 9 = 40
4) Suppose a random variable X has theprobability distribution with a: o 1 -2 0 1...
Put your answer in the blank (no explanation is required). 1) Consider the sample space S ={1,2,3,4,5,6,7,8,9,10), Ais the set of all odd numbers, B is the set of all even numbers, C is the set of numbers less than 5, D is (7,8) then BUD An (CU D)- 2) Put 3 balls into 4 boxes at random. The probability of that there is at most one ball in each box is 3) Suppose A and B are two independent...
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