Question

X and Y ar i.i.d. exponential random variables with mean = 2. Let Z = X + Y. The probability that Z is less than or equal to 3 is:

Answer 1

Answer :

Given data is :

There are two random variables X and Y.

Mean(X + Y) = = 4

Var(X + Y) = 8

then standard deviation = =

=

= 2.83

= 2.83

Now given condition is : P(Z <= 3)

Where Z = x+y = 3

P(x+y <= 3) =

= (3 - 4) / 2.83

= - 1 / 2.83

= - 0.35

From z table values,

P(x+y <= 3) = P(Z <= -0.35) = 0.3632