18.44 Chapter Notes - Chapter 7: Mit Opencourseware
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18. 440 problem set seven, due april 11: from textbook chapter five, theoretical exercise 26: if x is a beta random variable with parameters a and b show that. Var(x) = (a + b)2(a + b + 1: theoretical exercise 28: consider the beta distribution with parameters (a, b). Xn are independent if and only if their joint probability density (mass) function f(x1, . , xn) can be written as nn f(x1, . , xn) = gi(xi), for nonnegative functions gi(x), i = 1, . Cov(x + y, x y ) = 0: the following is one formulation of a famous two envelope paradox. Jill is a money-loving individual who, given two options, invariably chooses the one that gives her the most money in expectation. One day harry, a trusted (and capable of delivering) individual, o ers her the following deal as a gift. He will secretely toss a fair coin until the rst time that it comes up tails.
