Question 59693: please help me in this problem
for each of the following find constant c so that f(X) satisfies the condition of being apdf of one random variable x
1.f(X)=c(2/3)^x , x=1,2,3,...., zero elsewhere.
2.f(X)=cx, x=1,2,3,4,5,6 , zero elsewhere
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find constant c so that f(X) satisfies the condition of being apdf of one random variable x
1.f(X)=c(2/3)^x , x=1,2,3,...., zero elsewhere.
You haven't specified where X ends so I'll assume it ends at 6.
If that is true you get:
f(1)=(2/3)c
f(2)=(4/9)c
f(3)=(8/27)c
f(4)=(16/81)c
f(5)=(32/243)c
f(6)=(64/729)c
Add those up.
Set the sum = to 1
Solve for "c".
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2.f(X)=cx, x=1,2,3,4,5,6 , zero elsewhere
Same procedure as in #1.
Cheers,
Stan H.
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