Days 21 - 30

Sanderson M. Smith


Day #21:

"Education's purpose is to replace an empty mind with a closed one."


Review sheet provided. Two problem types emphasized:

(1) Premise: 70% of large population have ZIPPO. Pick random sample of size 10. Show the expected distribution of the random variable X if X is defined to be the number in the sample who have ZIPPO.

(2) Premise: Committee of 5 is randomly chosen from a group of 10 men and 22 women. Let X = the number of men on the committee. Show the expected distribution of the random variable X.

Day #22:

"It isn't that they can't see the solution. It is that they can't see the problem"


Test day.

Day #23:

"Research is the process of going up alleys to see if they are blind."


In text, read pages 407-410. Emphasis on mean of a discrete random variable. Work out the expected casino gain problems for the game of SPADES on the handout provided.

Day #24:

"An expert is a man who has made all the mistakes that can be made in a very narrow field."


Begin construction on the interactive spreadsheet for the casino game of SPADES. The spread should allow a user to input (1) the cost to play the game and (2) the payouts for a five card hand that contains x spades, where x is 0,1,2,3,4, or 5. The spreadsheet should calculate the casino's expected gain given the cost to play and the payouts. Spreadsheet should show two charts... one displaying the theoretical probabilities for x and the other (which will be interactive with the data) displaying the payouts.

Day #25:

""Everything should be made as simple as possible, but not simpler."


Complete the spreadsheet described on Day #24. Class activity involves insurance examples relating to expectation. One example: A life insurance company sells one-year policies that pay $100,000 to a beneficiary of a 30-year-old healthy purchaser if the purchaser dies within one year. The policy sells for $450. Suppose that reliable research indicates that 0.35% of purchasers can be expected to pass away during the next year. What is the insurance company's expected profit on each policy?

Day #26:

"It is a capital mistake to theorize before one has data."


Activity (Parents' Day Class): A bag contains 5 GREEN dice and 15 RED dice. You pay P dollars for the privilege to randomly select 4 of the dice from the bag. You win A dollars is the selected dice are all RED. You win B dollars if the selected dice are all GREEN. What is your expected net gain per game?

Day #27:

"For the things of the world cannot be made known without a knowledge of mathematics."


Activity and assignment built around problem 7.55 on page 431 in text. A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year is found in mortality tables. For ages 21, 22, 23, 24, and 25 the respective values are 0.00183, 0.00186, 0.00189, 0.00191, and 0.00193. The premium for the policy is $250. Find the company's expected earnings per policy. Assignment also involves a year-by-year analysis of expected premiums and claim payments.

Day #28:

"Numbers are intellectual witnesses that belong only to mankind."

-HONORE DE BALZAK (1799-1871)

Construct a spreadsheet that displays expected gains (based on $1) for each event in the game of ROULETTE. Class activity involves analyzing the game.

Day #29:

"I wish to God that these calculations had been executed by steam."

-CHARLES BABBAGE (1792-1871)

Work on ROULETTE spreadsheet. Class activity involved doing an analyis of 20SPOT KENO (as played at John Ascuaga's Negget, Reno).

Day #30:

"Try to be one of the people on whom nothing is lost."


Complete work on ROULETTE spreadsheet. Class activity involved a thorough analysis of the California Lottery game NINE SPOT KENO. It was discovered that the State of California makes approximately 54 cents on each dollar that is "invested" in NINE SPOT KENO.