STAB52H3 Lecture Notes - Lecture 9: Binomial Theorem, Independent And Identically Distributed Random Variables, Marginal Distribution
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Definition 3. 3. 1 the variance of a random variable x is the quantity where x = e(x) is the mean of x. Intuitively, the variance var(x) is a measure of how spread out the distribution of. Example 3. 3. 1 let x and y be two discrete random variables, with probability functions. Here, e(x) = 10 and var(x) = 0. Here, e(y) = 10 and var(y) = 25. Example 3. 3. 2 let x has probability function given by. Definition 3. 3. 2 the standard deviation of a random variable x is the quantity. Theorem 3. 3. 1 let x be any random variable, with expected value x = e(x) and variance var(x). Example 3. 3. 5 let w exponential( ), and let y = 5w + 3. Corollary 3. 3. 1 let x be any random variable, with standard deviation sd(x), and let a be any real number. Example 3. 3. 6 let w exponential( ), and let y = 5w + 3.
