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rizardon
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Homework Statement
2.5-13. Let x equal the number of flips of a fair coin that are required to observe heads-tails on consecutive flips
(a) Find the p.m.f. of x
(b) Determine the values of the mean, variance and standard deviation.
2.5-17. From 1999-2002 Red Rose Tea randomly placed one of 10 English porcelain miniature animals in a 100-bag box of Red Rose Tea, selecting from 10 endangered North American animals.
(a) On the average, how many boxes of tea must be purchased by a customer to obtain a complete collection consisting of 10 different animals.
Homework Equations
The Attempt at a Solution
2.5-13
(a) I wasn't sure what pattern the question was asking for, but judging from the answer given by the book
f(x) = (x-1)/2^x , for x = 2,3,...
I guess it meant a pattern in which a head is followed by a tail. But I don't get where the (x-1) comes from or is it by inspection from each trial.
(b) The mean is given by E(x) = The summation of x(f(x)) where x starts from 2 to infinity.
The problem is how do I sum x(f(x)). It is not a geometric series, is it?
2.5-17
(a)I'm guessing this is a geometric distribution in which X = # of purchases needed to get one success(all ten animals). The question is, how do I figure out the probability p?
In case this helps, the problems are from chapter 2.5 from "Probability and Statistical Inference 7th ed. by Hogg and Tanis".