**Unformatted text preview: **be drawn until one gets a cookie with at most one chocolate chip in it? What are the mean and standard deviation of this random variable? d) A bag of cookies has 2 cookies with at most one chocolate chip and 8 cookies with more than one chocolate chip. If Sarah and Sam split the bag evenly (5 cookies each) at random, what is the probability that Sarah gets both cookies with at most one chocolate chip? 8. Show that the binomial probability mass function for given n and p is unimodal in x. Unimodal means that either p(x) decreases as x increases or p(x) first increases to to some maximum at a particular x, (call it x ) and then is non-increasing as x goes from x 0 to n. Hint: Consider p(x+1)/p(x) (see equation 6.3 in the text). When p(x+1)/p(x) ≤ 1 then p(x) is non-increasing from x to x+1 and when p(x+1)/p(x) >1 then p(x) is increasing from x to x+1....

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- Spring '08
- KRIEGER
- Statistics, Standard Deviation, Probability theory, Chocolate chip cookie, Chocolate Chip, Problems section