Question

The random variable X has an Exponential distribution with parameter beta= 5. The
P(X > 18|X > 12) is equal to

Answer 1

Solution:

Given: X ~  Exponential distribution( beta= 5)

We have to find:

P(X > 18|X > 12) = ...........?

We use forgetfulness property of Exponential distribution.

P( X > a+b | X > a) = P( X > b)

thus 18 can written as 12+6

thus we get:

P(X > 18|X > 12) = P(X > 12 + 6 |X > 12)

....( according to forgetfulness property of Exponential distribution stated above)

We use cumulative distribution function of an Exponential distribution:

then

thus

thus

_{(Round final answer to specified number of decimal places)}