18.44 Lecture Notes - Lecture 11: Random Variable
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Lecture 11: binomial random variables and repeated trials. Toss fair coin n times. (tosses are independent. ) Can use binomial theorem to show probabilities sum to one: Number of heads is binomial random variable with parameters (n,p). Let x be number of heads you see. Then x is binomial with parameters (n, p) given by (6, 1/2). Probability mass function for x can be computed using the 6th row of pascal"s triangle. If coin is biased (comes up heads with probability p 1/2), we can still use the 6th row of pascal"s triangle, but the probability that x = i gets multiplied by. Answer: use binomial formula with p = 1/7 and q = 1 p = 6/7. Compute the probability that nobody was born on a tuesday. Let x be a binomial random variable with parameters (n, p). Direct approach: by de nition of expectation, e[x] =
