Question

Suppose that the time, in hours, taken to repair a heat pump is a random variable X having a gamma distribution with parameters alpha=2 and beta=1/2. What is the probability that the next service call will

require:
at most 1 hour to repair the heat pump?

Answer 1

To find the probability that the next service call will require at most 1 hour to repair the heat pump, we need to calculate the cumulative distribution function (CDF) of the gamma distribution with parameters alpha=2 and beta=1/2. Using the CDF, we can find the probability by plugging in the value of 1 for x in the formula: P(X ≤ 1) = 1 - Γ(2, 1/2). The probability is approximately 0.6065.

Step-by-step explanation:

To find the probability that the next service call will require at most 1 hour to repair the heat pump, we need to calculate the cumulative distribution function (CDF) of the gamma distribution with parameters alpha=2 and beta=1/2.

Using the CDF, we can find the probability by plugging in the value of 1 for x in the formula: P(X ≤ 1) = 1 - Γ(2, 1/2).

Using a calculator or software, we can find that the probability is approximately 0.6065.