Let X be a discrete random variable that takes value -2, -1, 0, 1, 2 each...

Let X be a discrete random variable that takes value -2, -1, 0, 1, 2 each with probability 1/5.

Let Y=X²

a) Find the possible values of Y. Construct a joint probability distribution table for X and Y. Include the marginal probabilities.

b) Find E(X) and E(Y).

c) Show that X and Y are not independent.

Expert Solution

a) for Y is mapped on X

therefore possible value of X are {(-2)²,(-1)²,0²,1²,2²} ={ 4,1,0,1,4) ={0,1,4}

below is joint probability distribution of X and Y:

	y			P(y)
x	0	1	4	Total
-2	0	0	1/5	1/5
-1	0	1/5	0	1/5
0	1/5	0	0	1/5
1	0	1/5	0	1/5
2	0	0	1/5	1/5
P(x)	1/5	2/5	2/5	1.0000

margnial probabilities are in P(X) row and P(y) column

b)

E(X)=-2*(1/5)+(-1)*(1/5)+0*(1/5)+1*(1/5)+2*(1/5)=0

E(Y)=0*(1/5)+1*(2/5)+4*(2/5)=2

c)

here as P(X=-2,Y=0)=0 while P(X=-2)*P(Y=0)=(1/5)*(!/5)=1/25

as they both are not equal; X and Y are not independent,

orchestra answered 1 year ago

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