The lifetime T of a certain device in 1000 hour units has th

The lifetime T of a certain device (in 1000 hour units) has the exponential distribution with parameter ½. Find P(T > 2).

Solution

Given that T is the lifetime of a certain device.

T has Exponential distribution with paramter with parameter 1/2.

We have to find the P(T > 2).

The p.d.f. of T is,

f(T) = e^-t   t > 0 and > 0.

given that = 1 / 2 = 0.5

P(T>2) = f(T) dt (from 2 to )

= e^-t dt

=   e^-t dt

= [  e^-t / - ]

= - / [ e^- - e^-0.5*2 ]

= - [ 0 - 0.3679 ]

P(T >2) = 0.3679