STAT 100A Lecture Notes - Lecture 14: Random Variable, Geometric Distribution
Document Summary
De nition each having probability of success 0 < p < 1, are performed until a success occurs. If x is the number of trials required, then x is said to have a geometric distribution. Alice eats cookies one after another until she nds and a chocolate cookie. For each cookie, the probability of the cookie being a chocolate cookie is 1. P(x 13|x > 5) = p(x > 12|x > 5) Therefore, the fact that alice has already eaten 5 cookies does not a ect the probability of her eating at least 8 more cookies. Therefore, iqi 1p (i 1 + 1)qi 1p (i 1)qi 1p + (i 1)qi 1p + (i 1)qi 1p + qi 1p (cid:2)i=1 p. 1 (1 p) (i 1)qi 1p + 1. E(cid:9)x 2(cid:10) = i2qi 1p (i 1)2qi 1p + (i 1 + i)2qi 1p (cid:2)i=1 (cid:2)i=1 (cid:2)i=1 (cid:2)j=0.
