STA 2023 Lecture Notes - Lecture 14: Sickle-Cell Disease, Random Variable, Standard Deviation
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Draw 10 cards with replacement from a deck of 52 cards. Let x = number of hearts in 10. Is x a binomial random variable: 10 identical trials, 2 outcomes heart, not heart, p = 13/52, q = 39/52, independent, x is binomial. Without replace(cid:373)e(cid:374)t: not 10 identical trials, 2 outcomes heart, no heart, p, q do not remain constant, not independent, x is not binomial. Let x = number of children in 3 that get sickle cell anemia. Is x a binomial random variable: 3 identical trials, only 2 outcomes get sca or do(cid:374)"t, p = , q = , independent, x is binomial. To find binomial random variable probabilities: use methods from ch. = (1)(1)(27/64) = 27/64 p(x = 0) = 3!/(3-0)! x (1/4)0(3/4)3 p(none) p(exactly 1) = 3!/(3-1)! = (3)(1/4)(9/16) = 27/64: binomial tables in back of book (pages 812 815). X is binomial n = 15 p = 0. 3: at most 3 (x 3) table.
