Use R to generate random number samples.

The life time of a laser (in hours) is exponentially distributed with lambda= 1/80. Two such

lasers are operating independently.

a) Use a simulated sample of size 1000 to estimate the probability that the sum of the two

lifetimes is greater than 100 hours.

b) Estimate the probability that the both lasers last more than 50 hours.

Notes:

To generate random numbers you use the following R commands:

a) uniform distribution- runif(n, min=0, max=1)

b)gamma distribution rgamma(n, shape=alpha, scale=beta)

c) exponential distribution rexp(n, lambda)