18.44 Lecture Notes - Lecture 10: Dried Lime, Elche, Random Variable
Document Summary
The variable of x, denoted var(x), is de ned by var(x) = e[(x - ) ] Taking g(x) = (x - ) , and recalling that e[g(x)] = (x - ) p(x), we nd that var[x] = (x - ) p(x) Variance is one way to measure the amount of random variable varies from its mean over successive trials. Let x be a random variable with mean . We introduced the formula var[x] = e[(x - ) ] This can be written var[x] = e[x - 2x + ] This gives us our very important alternate formula: var[x] = e[x ] - ( [ ]) . By additivity of expectation, this is the same as e[x ] - 2 e[x] + = e[x ] - . The original formula gives intuitive idea of what variance is (expected square of difference from mean) But we will often use this alternate formula when we have to actually compute the variance.
