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freshysans4
03.03.2020 •
Mathematics
The pair of random variables (X,Y) is equally likely to take any of the four pairs of values (0,1), (1,0), (−1,0), (0,−1). Note that X and Y each have zero mean.
a) Find E[XY].
E[XY]=
b) YES or NO: For this pair of random variables (X,Y), is it true that Var(X+Y)=Var(X)+Var(Y)?
Select an option Yes No
c) YES or NO: We know that if X and Y are independent, then Var(X+Y)=Var(X)+Var(Y). Is the converse true? That is, does the condition Var(X+Y)=Var(X)+Var(Y) imply independence?
Select an option Yes No
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Ответ:
Answer and Step-by-step explanation:
(a)
E[XY] = 1/4*0*1 + 1/4*1*0 + 1/4*-1*0 +1/4*0*-1 = 0
(b)
E[X] = 0, E[Y] = 0
Thus, Cov(X,Y) = E[XY] - E[X]E[Y] = 0
So, Var(X + Y) = Var(X) + Var(Y) is True
The answer is Yes
(c) No, the converse is not true
Ответ:
7745.2
Step-by-step explanation:
you need to multiply 67 by 578 which is 38726. then you divide it by 5. In short, you can just use calculator or you can use scratch paper.\