Question

(15 points) A manufacturer is studying the length of time required by a maintenance team to respond to reported failure of a specific machine in the plant. The plant manager wants to know the percentage of repair calls answered within 10 minutes. 2. The response time, X, measured in minutes is known to have an exponential distribution. For the exponential distribution, as λ increases what happens to the mean and variance of the distribution? 4 points) Draw a sketch of the graph showing a curve for the probability distribution if the response time, X, is an exponential random variable with A-a. On the same sketch draw a curve indicating the probability density function if λ increases to λ-2a. (2 points) If the response time X is an exponential random variable with A-a, write an expression for the corresponding probability density function? (2 points) How does the mean and variance depend on the parameter, λ ? (1 points) what is the standard deviation for λ=r? and λ2r? (2 points) what is the cumulative probability distribution for λ.r? 4 points) Draw a sketch of the curve for the cumulative probability function showing the relationship between the cumulative probability function and the response time. On the curve indicate the probability corresponding to a response within 10 minutes?

Answer 1

Po, expl) → 个子(%) ↓去 느a ズ、 Meano, 万 → exp (A): A inoxeasts, mean and varsoe decreas

→ Cumaalive dishibudionfundion- f,(x) = "X 2 e 0 ら(x): 1-e 1. Cot メ Fiz)