Question 59211: please helps in this
let the pdf f(x) be positive at x=-1,0,1 and zero else where
1. if f(0) = 0.25 , find E(x^2)
2. if f(0) = 0.25 and if E(X) =0.25 , determine f(-1) and f(1)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! let the pdf f(x) be positive at x=-1,0,1 and zero else where
1. if f(0) = 0.25 , find E(x^2)
Let f(-1)=x
The f(1)=0.75-x
E(X^2)=(0^2)*0.25+(-1)^2*x+(1)^2*(0.75-x)
E(X^2)=0+x+(0.75-x)
=0.75
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2. if f(0) = 0.25 and if E(X) =0.25 , determine f(-1) and f(1)
Let f(-1)=x
Then f(1)=(0.75-x)
E(X)=0*0.25+(-1)x+(1)(0.75-x)=0.25
-x+0.75-x=0.25
-2x=-0.5
x=0.25
So, f(-1)=x=0.25
f(1)=(0.75-x)=0.75-0.25=0.50
Cheers,
Stan H.
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