Introduction to Statistical Methods for the Life and Health Sciences
Instructor: Ivo Dinov, Asst. Prof.
Departments of Statistics & Neurology
Friday, Nov. 16, 2001, turn in after lecture
submission rules. On the front page include the following
(HW_5_1) The casino game of Tai Sai is played by betting
on various possible combinations of results when three dice are
rolled. One possibility is to place a bet on a single number. In this case,
the more times this number appears on the three dice, the greater the winnings.
Here's an example of how it works: Consider a gambler who wishes
to bet on the number six. For each dollar bet, the player wins twelve
times his/her stake if three sixes are rolled on the three dice, two times
his/her stake if two sixes are rolled on the three dice or one times his/her
stake if only one six is rolled on the three dice. If no sixes are rolled,
then the stake is lost.
Let X be the return from a single bet with a $5 stake. X
has the following probability function:
Compute E[X], sd[X] and the probability of making a positive return
from a single bet.
A player will make a profit overall if their mean return from placing a
series of bets is positve. Let X_bar be the mean return from 100
separate bets with a $5 stake.
What are the values of E[X_bar] and SD[X_bar]?
What is the approximate distribution of X_bar? What theorem was
needed to decide this?
Calculate the probability of, on average, making a positive return from
placing one hundred separate bets with $5 stakes.
Repeat the calculations above using 1,000, 5,000 and 10,000
Create a scatter plot of probability that the mean return from playing
Sai is positive (on y-axis) versus number of bets (on x-axis).
Comment on what the plot appears to show.
\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology,
UCLA School of Medicine/