STAT 1000 Lecture Notes - Lecture 26: Random Variable, Standard Deviation, Binomial Coefficient
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The observations are fixed . . there are 50. Whether or not one person has a boy does not influence what another person will have. The observations fall into two categories . . boy or girl. The probability of having a boy or girl is 50% There is a fixed number of observations 10. There is a success or failure response heads or tails. The probability = 1/2 is the same every time. There is a fixed number of observations 25. There is a success or failure response hearts or not. The trials are all independent of one another. The probability = 13/52 is the same every time. If a population contains a proportion of p success, the count x of success in the sample. We say our random variable x is approximately binomially distributed with parameters n (fixed sample size) and p (proportion or probability of successes. )