Question

[4G-07] Three individuals are completing a given task. The completion time for each individual is exponential random variable with mean 7, and is independent of one another. Find the probability that the first person to complete the task will do so in less than 5 minutes. (Use 4 decimals)

Answer 1

P(X≤5) = 0.5105 (Approx)

Explanation:

Assume, x = completion time of given task

Mean u = 7

So,

λ = 1/u = 1/7

So,

x ↔ exp(λ)

f(x) = P(X≤x) =
`1-e^{-(1)/(u)x }`

P(X≤5) =
`1-e^{-(1)/(7)5 }`

P(X≤5) = 0.5105 (Approx)