Question

5. (2 + 3 + 3 marks) A firm receives number of calls per day that follows Poisson distribution with mean 0.8. Find the probability that the number of calls a. on the 4th day is 2 b. on the first 8 days totals 5. c. in the first 6 hours totals at least 2.
4.(4 + 3 marks) In an ordinary deck of 52 playing cards, if a person draws a king or a jack, he is paid $10; if he draws a queen, he is paid $5.If he draws any other card, he will pay $4. a. If X is the gain for the person who plays the game, construct a probability distribution for X. b. Find the expected gain?

Answer 1

We would be looking at the first question here all parts as:

Q5) The distribution given here is:

a) The probability of having 2 calls on the 4th day is computed here as:

Therefore 0.1438 is the required probability here.

b) Average number of calls in 8 days is computed here as:
= 8*0.8 = 6.4

Therefore probability of having 5 calls in 8 days is computed here as:

Therefore 0.1487 is the required probability here.

c) For 6 hours period that is 6/24 = 0.25 day, averge number of calls is given as: 0.25*0.8 = 0.2

Therefore the probability that there are in the first 6 hours total calls at least 2 is computed here as:

Therefore 0.0175 is the required probability here.