Four electronic ovens that were dropped during shipment are inspected and classifi ed as containing either a major, a minor, or no defect. In the past, 60% of dropped ovens had a major defect, 30% had a minor defect, and 10% had no defect. Assume that the defects on the four ovens occur independently. 

(a) Is the probability distribution of the count of ovens in each category multinomial? Why or why not?

(b) What is the probability that, of the four dropped ovens, two have a major defect and two have a minor defect?

(c) What is the probability that no oven has a defect?

Determine the following:

(d) Joint probability mass function of the number of ovens with a major defect and the number with a minor defect

(e) Expected number of ovens with a major defect

(f) Expected number of ovens with a minor defect

(g) Conditional probability that two ovens have major defects given that two ovens have minor defects

(h) Conditional probability that three ovens have major defects given that two ovens have minor defects

(i) Conditional probability distribution of the number of ovens with major defects given that two ovens have minor defects

(j) Conditional mean of the number of ovens with major defects given that two ovens have minor defects.