STAB52H3 Lecture Notes - Lecture 5: Absolute Continuity, Probability Distribution, Exclusive Or
Document Summary
Let x be a random variable with a known distribution. Suppose that y = h(x), where h: r1 r1 is some function. Here, y is also a random variable as for s s. Theorem 2. 6. 1 let x be a discrete random variable, with probability function px. Let y = h(x), where h : r1 r1 is some function. Then y is also a discrete random variable, and its probability function py satisfies where h 1{y} is the set of all real numbers x with h(x) = y. Example 2. 6. 1 let x be the number of heads when flipping three coins. Here, x counts the number of heads when flipping three coins. Furthermore, h (0) = 0 which gives h 1 {0} = {0}. P(y = 0) = p(x = 0) = 1/8. Moreover, h (1) = h (2) = h (3) = 1 which gives h 1 {1} = {1, 2, 3}.
