Probabilities 3

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Probabilities 4

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statistics

Airline company officials find that 86% of all people who make reservations show up for their flights. If an airline has accepted 240 reservations and if there are 213 available seats, find the probability that the airline will have a seat for each person who has reserved one and who shows up.

Differential operators

Problem attached.

Eigenvalue problem

Problem attached.

Green's function for an eigenvalue problem

Problem attached.

Game Theory

In the two-player game of Two Stacks, a deck of cards (with the joker added, for a total of 53 cards) is randomly divided into two piles. The two players take turns removing cards from one pile or the other. On a player's turn, that player may remove any positive number of cards from a single pile. The object of the game is to r ...continues

Obtaining orthonormal eigenfunctions

Problem attached.

RSA Cipher

Alice chooses two large prime numbers p and q. She finds their product, m=pq which is public. She also finds n= (p-1)(q-1) which is private. She chooses e which is a number relatively prime to n and finds d= the inverse of e (mod n). The number e is public and the number d is private. When Bob wants to send a message x (a number ...continues

Congruency

solve for a and b 4a + b = 1 (mod 5) a + b = 2 (mod 5) check answers for a and b by substituting into the original equations