Problem : Let
X have a uniform distribution on the interval (1; 3).What is the proba-
bility that the sum of 2 independent observations of X is greater than 5?
Let X1 and X2 be the two independent obeservations.
We have to show P(X1+X2 > 5)=1- P(X1+X2 <=5).
Here f(x1,x2)=1/2 for 1<x1,x2<3
= 0 otherwise
(Is the joint pmf and its range correct??? )
here x1 varies from 1 to 3 and x2 varies from 1 to 5-x1.
Now P(x1+x2<=5)= integral (1<x1<3) integral (1<x2< 5-x1) of 1/2 dxdy
on solving this i am getting answer 2....which is wrong( as probablity can not be more than 1)
the right answer of P(X1+X2 >5)=1/8...
Where i am going wrong please let me know...