Question

EXPUNENTAL
DISTRIBUTI
9-59. Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter λ = 2, time being measured in minutes. What is the probability that a shower will last more than three minutes ? If a shower has already lasted for 2 minutes, what is the probability that it will last for at least one more minute ?​

Answer 1

Answer:

P(X > 3min) = 0.002478

P( X >= 3 / X = 2) = 0.135335

Step-by-step explanation:

X has an exponential distribution with parameter λ = 2

pdf of X => f(x) = λe^(-λx) = 2e^(-2x)

cdf of X => F(x) = 1- e^(-λx) = 1-e^(-2x)

P(X > 3) = 1 - F(3) = e^(-(2 * 3)) = e^(-6) = 0.002478

P( X >=3 / X=2) = P( X >= 1) => Lack of memory property

P(X >= 1) = 1 - F(1) = e^(-2) = 0.135335