Question

P{X=k}=c|k|for k =-2,-1,1,2 and Y=max(0,X) where max means maximum. Thus, max(0,-3)=0, and max(0,3)=3. Commute the following.

a) E[X]

b) E[max(0,X)]

c) P{Y=0}

Answer 1

P{X=k}=c|k|  

P{X=-2}=2c

P{X=-1}=c

P{X=+1}=c

P{X=2}=2c

,   

a)

k	-2	-1	1	2	TOTAL
P(X=k)	1/3	1/6	1/6	1/3	1
k*P(X=k)	-2/3	-1/6	1/6	2/3	0

,   

b)

Let,Y=max(0,X)

X	-2	-1	1	2
Y	0	0	1	2

Clearly, Y has 3 mass-points i.e., 0,1,2

P(Y=1)=P(X=1)=1/6

P(Y=2)=P(X=2)=1/3

P(Y=0)=P(X=-1)+P(X=-2)=1/6+1/3=3/6=1/2

c) P(Y=0)=P(X=-1)+P(X=-2)=1/6+1/3=3/6=1/2

I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)