Suppose that the time, in hours, required to repair a heat pump is a random variable X having a gamma distribution with parameters a = 2 and ß =. What is the probability that on the next service call (a) at most 3 hours will be required to repair the heat pump? (b) at least 4 hours will be required to repair the heat pump?

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Please help me solve both a and b. Please do not round the answer and write the full number given. if you could also show your steps because I am slightly confused. Thank you so much and I will be glad to rate you. 

Suppose that the time, in hours, required to repair a heat pump is a random variable \( X \) having a gamma distribution with parameters \( \alpha = 2 \) and \( \beta = \frac{1}{2} \).

What is the probability that on the next service call:

(a) at most 3 hours will be required to repair the heat pump?

(b) at least 4 hours will be required to repair the heat pump?
Transcribed Image Text:Suppose that the time, in hours, required to repair a heat pump is a random variable \( X \) having a gamma distribution with parameters \( \alpha = 2 \) and \( \beta = \frac{1}{2} \). What is the probability that on the next service call: (a) at most 3 hours will be required to repair the heat pump? (b) at least 4 hours will be required to repair the heat pump?
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