Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 98
Problems
Оглавление1 3.4.1 Show that if then(i) Use the definition of binomial coefficients as ratios of the factorials. (ii) Use directly the interpretation of the binomial coefficients as the number of subsets of a given size. (iii) How many ways can one choose an ‐element subset from a ‐element subset from a ‐element subset from a ‐element subset from a element set? (where ).
2 3.4.2 Find the coefficient of the term in the expansion of .
3 3.4.3 Use the argument analogous to that in Theorem 3.3.2 to show that if , and , then
4 3.4.4 Use Stirling's formula to approximate the number of ways: (i) A set of size can be partitioned into two equal parts. (ii) A set of size can be partitioned into three equal parts.
5 3.4.5 Approximate the probability that every state will be represented in the committee in Problem 3.3.1 (i).