Unformatted text preview: 1. As before, continue drawing balls until the ﬁrst red is drawn. However, this time, each time a ball is drawn it is returned to the urn along with k more of the same colour. The problem done in class corresponds to the case where k = 1. Is it true that E ( X ) = ∞ for all values of k ? 2. Chapter 4 Theoretical Exercise 31 (29 in 6th edition). 3. The probability of throwing a 6 with a biased die is p , where 0 < p < 1. Three players A , B , and C take turns rolling this die, starting with A , then B , then C . The ﬁrst one to throw a 6 wins. (a) Find the probability of winning for players A , B , and C . (b) If X is a random variable which takes the value r if the game ﬁnishes with the r th throw, ﬁnd the probability mass function for X , and evaluate E ( X ) and V ar ( X ). 4. Chapter 4 Theoretical Exercise 20. 5. Chapter 4 Theoretical Exercise 28 (26 in 6th edition)....
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 Spring '09
 M.Tao
 Math, Probability, Probability theory, Probability mass function, green balls

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