Thetime(inhours) an exponentially distributed random variable with parameter λ = 1 . what is 2 (a) the probability that a repair time exceeds 2 hours? (b) the conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours?

a) 0.1353

b) 0.3679

Step-by-step explanation:

Let's start by defining the random variable T.

T : ''The time (in hours) required to repair a machine''

T ~ exp (λ)

T ~ exp (1)

The probability density function for the exponential distribution is

(In the equation I replaced λ = L)

With L > 0 and x ≥ 0

In this exercise λ = 1 ⇒

For a)

For b)

The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur

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the answer is 62.8 cubic units