GIVEN :
Distribution of given random variable X:
random variable X | -1 | 3 |
Probability | 3/4 | 1/4 |
Distribution of given random variable Y:
random variable X | -3 | 2 |
Probability | 1/2 | 1/2 |
WE KNOW THAT:
a)
So, E[X] = (-1*3/4) + (3*1/4)
= -3/4 + 3/4 = 0
So, E[Y] = (-3*1/2) + (2*1/2)
= -3/2 + 2/2 = -1/2
E[X] = 0, And
E[Y] = -1/2
Also,
E(X+Y) = E(X) + E(Y) |
so , from these moment generating functions
E[X+Y] = 0 + (-1/2) = -1/2
E[X+Y] = -1/2
b)
we know that
where is the expected value.
Also,
Also,
Var(X + Y) = Var(X - Y) = Var(X) + Var(Y) |
Var(X+Y) = 3 +9/4
Var(X+Y) = 5.25
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Random variables X and Y have following distributions. P(X = -1) = 3/4, P(X = 3)...
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