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Unformatted text preview: 1.2. DISCRETE PROBABILITY DISTRIBUTIONS 39 26 Two cards are drawn successively from a deck of 52 cards. Find the probability that the second card is higher in rank than the first card. Hint : Show that 1 = P (higher) + P (lower) + P (same) and use the fact that P (higher) = P (lower). 27 A life table is a table that lists for a given number of births the estimated number of people who will live to a given age. In Appendix C we give a life table based upon 100,000 births for ages from 0 to 85, both for women and for men. Show how from this table you can estimate the probability m ( x ) that a person born in 1981 would live to age x . Write a program to plot m ( x ) both for men and for women, and comment on the differences that you see in the two cases. *28 Here is an attempt to get around the fact that we cannot choose a “random integer.” (a) What, intuitively, is the probability that a “randomly chosen” positive integer is a multiple of 3? (b) Let P 3 ( N ) be the probability that an integer, chosen at random between 1 and N , is a multiple of 3 (since the sample space is finite, this is a legitimate probability). Show that the limit P 3 = lim N →∞ P 3 ( N ) exists and equals 1/3. This formalizes the intuition in (a), and gives usexists and equals 1/3....
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This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.
- Spring '09