![Suppose that Y is an exponential random variable with = 2.
Find P[Y > E(Y) + 2 Var(Y)]
Solution
E(Y )=1/=1/2
Var(Y )=1/ ^2=1/4
P[Y > E(Y ) + 2 + Var(Y )]=P[Y > 1/2+ 2 + 1/4]=P[Y >2.75]
=integral from 2.75 to ( e^(-?t))dt
=[-e^(-t)/] from 2.75 to =e^(-(2.75))
=e^(-2(2.75))=e^(-(5.5))=0.00409](https://image.slidesharecdn.com/supposethatyisanexponentialrandomvariablewith2-230402050648-7012c2b5/85/Suppose-that-Y-is-an-exponential-random-variable-with-2-Find-P-pdf-1-320.jpg)
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Suppose that Y is an exponential random variable with = 2. Find P.pdf
- 1. Suppose that Y is an exponential random variable with = 2. Find P[Y > E(Y) + 2 Var(Y)] Solution E(Y )=1/=1/2 Var(Y )=1/ ^2=1/4 P[Y > E(Y ) + 2 + Var(Y )]=P[Y > 1/2+ 2 + 1/4]=P[Y >2.75] =integral from 2.75 to ( e^(-?t))dt =[-e^(-t)/] from 2.75 to =e^(-(2.75)) =e^(-2(2.75))=e^(-(5.5))=0.00409