ECO220Y1 Lecture Notes - Lecture 8: Mutual Exclusivity, Random Variable, Bernoulli Distribution
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Random variable: assigns number to outcome of an experiment. Continuous random variable: takes an uncountable (infinite) number of values (sample mean) Discrete random variable: takes a countable (finite) number of values. Continuous vs discrete is not non-integer vs integer. Is about how many possible values there are. Distribution of sample statistics shows how much sampling noise. Binomial random variable is number of successes in binomial experiment. Binomial distribution gives probability of each value of x. 2 = v[x] = e[x - ]2 = (x- )2 * p(x) E[a + bx + cy] = a + be[x] + ce[y] V[a + bx + cy] = b2v[x] + c2v[y] + 2bccov[x,y] Bernoulli random variable equals 1 if success and 0 if failure. Success (p) or failure (1-p: e[x] = 0*(1-p) + 1*(p) = p, v[x] = p(1-p)2 + (1-p)(0-p)2 = p*(1-p) Assume outcome across trials are independent p is constant.
