Question

11.ExponentialDistribution 1: Problem 4 Previous Problem Problem List Next Problem (1 point) Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter 1-0.6. What is (a) the probability that a repair takes less than 4 hours? (b) the conditional probability that a repair takes at least 10 hours, given that it takes more than 9 hours? Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining Email instructor

Answer 1

Cumulative distribution function

$F_X(x)=1-e^-\lambda x$

=

a.)

P(X <4)- Fx(4)

- 0.6 4 * 1-e

0,9093

b.)

$P(X\geq 10/X>9)=P(X\geq 9+1/X>9)$

P(X > 10/X > 9) PX 1)

P(X > 10/X > 9)-1-P(X < 1)

1 - [1- e-0.6-1

$=e^-^0^.^6^*^1$

$=0.5488$