QUESTION c i calculate the expected number of dents in a ti

QUESTION:

c) i ) calculate the expected number of dents in a tin delievered by truck 1, E(X|T=1)

ii) Calculate the expected number of dents in a tin delievered by truck 2, E(X|T=2)

iii) How many dents would one expect to find in randomly chosen tin?

d) if a tin chosen at random has two dents in it, what is the probability that it was delievered by truck 1?

e) A truck crew\'s carefulness is judged by selecting three tins at random from the corresponding truck and observing how many dents are in them, if each of the three chosen tins has no more than one dent in it, then the crew is considered eligible for the perfect peaches prize. what is the probability that the crew of truck 2 found to be eligible?

Question 3. Tinned peaches are delivered to a shop by two different trucks. Let the trucks be numbered 1 and 2, and let T be the random variable that represents the truck\'s number. It is observed that the tins of peaches have up to three dents in them. Let X be the random variable that represents the number of dents in a tin. The table below represents the joint probability mass function for a randomly chosen tin. 8 16 16 8 3 16 16 (a) (i) Copy down the table and fill in the marginal distributions. (i) What does the marginal distribution of T tell us? What is it called? (b) Is the number of dents in a tin independent of the truck that delivered it? (c) () Calculate the expected number of dents in a tin delivered by truck 1, E(XIT 1). (ii) Calculate the expected number of dents in a tin delivered by truck 2, E(XIT 2) (ii) How many dents would one expect to find in a randomly chosen tin? (d) If a tin chosen at random has two dents in it, what is the probability that it was delivered by truck 1? (e) A truck crew\'s carefulness is jadged by selecting three tins at random from the corresponding truck and observing how many dents are in them. If each of the three chosen tins has no more than one dent in it, then the crew is considered eligible for the Perfect Peaches Prize. What is the probability that the crew of truck 2 is found to be eligible?

Solution