Question

Problem 10: 10 points Assume that the distribution of the lifetime of a certain appliance is given. Knowing that the device has served five years, find the chance that it will serve 5 more years 1. Assume that the lifetime, T, is exponentially distributed, with the mean equal to 25 years. 2. How will your answer change if the lifetime (T) is uniformly distributed over the interval, (0,25)?

Answer 1

1)

P(X > 10| X> 5)

= P(X > 5 ) {due to memoryless property of exponential distribution}

= e^(-5/25)    {P(X > x) = e^(- x/mean)}

= 0.81873

2)

P(X > 10|X> 5)

= P(X > 10) /P(X >5)

= (25 - 10)/(25 -5)

= 0.75