Question

The waiting time (in hours) between consecutive hospital emergency visits during a pandemic is modeled as an Exponential random variable with \lambda=0.5λ=0.5. Let X be the waiting time observed at a hospital in city A. Let Y be the waiting time observed at a hospital in city B. Assume that waiting times are independent across hospitals in different cities.

(a). Find E\left( X+Y \right)E(X+Y) and E\left(XY\right)E(XY).

(b). Let y_1,y_2,.......,y_{25}y1​,y2​,.......,y25​ be a random sample of 25 waiting times at the hospital in city B. The sample mean was \overline{y}=2.8y​=2.8. Assuming \lambdaλ is unknown, what is the maximum likelihood estimate of \lambdaλ?

Answer 1

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