Explain how to estimate the following probabilities. (a) P{X > Y}, where X and Y

Question

Explain how to estimate the following probabilities.

(a) P{X > Y}, where X and Y are independent Poisson random variables with parameters 3 and 5, respectively.

(b) The probability of a royal-flush (a ten, a jack, a queen, a king, and an ace of the same suit) in poker, if 5 cards are selected at random from a deck of 52 cards.

(c) The probability that it will take more than 35 minutes to have your oil filter changed in Exercise 5.6. (d) With probability 0.95, we need to estimate each of the probabilities listed in (a-c) with a margin of error not exceeding 0.005. What should be the size of our Monte Carlo study in each case?

(e) (Computer mini-project) Conduct a Monte Carlo study and estimate probabilities (a-c) with an error not exceeding 0.005 with probability 0.95.

Explanation / Answer

Solution:-

b)

The probability that the hand is a royal flush is 0.00000154.

Total combination of royal flush = 4

Total number of combinations of different hands = 52C5

Total number of combinations of different hands = 2,598,960

The probability that the hand is a royal flush is = 4/2598960

The probability that the hand is a royal flush is = 0.00000154.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.