ECON2209 Lecture 9: 10February_EconStats_Karagodsky
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Mean = e[x] = np variance = var(x) = np(1-p) 1. 1 probability of 4 heads from 4 coin tosses. Pr(x = 0 | n = 4, p = . 5) Note: here the | line doesn"t mean conditional. 54(1 . 5)0 = 1 . 54 1 = 6. 25. Continuous random variables (think in terms of area under a curve) P(x) is the probability density function function f(x). (b-a)f(x) = 1, f(x) = 1 b a. Implications: any equal sized interval will have the same probability of occurring 2. f(x) Mean of a uniform distribution: n = a+b. Standard deviation of uniform dist: =q (b a)1. Expected value: e[x] = r b a (x )2dx. If a random variable is uniformly distributed from 10 to 2 what is f(x)? a f (x)(x )2dx f(x)(10-2) = 1 f(x) = 1. 4 normal distribution here, is the expected val. Note: birth weight follows an approximately normal distribution with n(5. 54,
