Probability Distribution

1. Classify the following random variables as discrete or continuous.

A. The number of units of some product sold on a given day

B. The number of correct answers in a 25-item question test

C. The length of time to play 12 holes of golf

D. The number of eggs laid each month by 1 hen

E. The length of life (in hours) of a light bulb

F. The number of vehicular accidents each year in Metro Manila

G. The weight of grain in kilograms produce per hectares

2. Solve each of the following problems:

1) By investing in a particular stock, a businessman can make a profit in 1 year of P200,000 with probability of 0.4 or take a loss of P50,000 with probability of 0.60. What is the businessman's expected gain?

2) In a gambling game, a man is paid P50 if he draws a jack or queen and P100 if he draws a king or ace from an ordinary deck of 52 playing cards. If he draws any other card, he loses. How much should he pay to play if the game is fair?

3) A resident purchases an apartment dweller's insurance at P6,250 per year with her furnishings insured up to maximum of P500,000. The insurance company from the past experience feels that the probabilities of claims of P25,000, P50,000, P250,000, P500,000 are respectively, 0.1, .02, .01, .001. Can the insurance company be expected to make a profit of P500 per policy?

4) If a man purchases a raffle ticket, he can win a first price of P50,000 or a second price of P20,000 with probabilities 0.001 and 0.003. What should be the fair price for the ticket?

5) In a given business venture, a man can make a profit of P300,000 with probability of 0.6 or take a loss of P100,000 with probability of 0.4. Determine his expectation.

6) If you have a probability of gaining P20,000, 35probability of losing P25,000, and a 320probability of breaking even, what is your expected value?

7) Mr. Roldan is planning to open a business. His friend told him that the business has 35probability of gaining P450,000 and a 25probability of losing P300,000. What is Mr. Roldan's expected value for his business?

8) The Leicarl's Construction Company bids on a job to construct a building. If the bid won, there is a 0.7 probability of making a P9,500,000 profit and a probability of 0.3 that the construction will break even. Determine the expected value of the company.

9) A 25-year old woman decides to pay P12,000 for a one-yea life insurance policy with coverage of P500,000. The probability of her living through the year is 0.0995. What is her expected value for the insurance policy?