Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137538461
Author: Robert Hogg, Elliot Tanis
Publisher: PEARSON+
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Chapter 2.3, Problem 16E

Let X equal the number of flips of a fair coin that are required to observe the same face on consecutive flips.

(a) Find the pmf of X. HINT: Draw a tree diagram.

(b) Find the moment-generating function of X.

(c) Use the mgf to find the values of (i) the mean and (ii) the variance of X.

(d) Find the values of (I) P ( X ≤ 3 ) , (ii) P ( X ≥ 5 ) , and (iii) P ( X = 3 ) .

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Chapter 2 Solutions

Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

Ch. 2.1 - Let the pmf of X be defined by f(x)=x9,x=2,3,4.....Ch. 2.1 - Let a chip be taken at random from a bowl that...Ch. 2.1 - For each of the following, determine the constant...Ch. 2.1 - Let X be a discrete random variable with pmf...Ch. 2.1 - The pmf of X is f(x)=(5x)10,x=1,2,3,4. (a) Graph...Ch. 2.1 - The state of Michigan generates a three-digit...Ch. 2.1 - Let a random experiment be the casting of a pair...Ch. 2.1 - Let a random experiment consist of rolling a pair...Ch. 2.1 - Let the pmf of X be defined by...Ch. 2.1 - A fair four-sided die has two faces numbered 0 and...
Ch. 2.1 - Let X be the number of accidents per week in a...Ch. 2.1 - A bag contains 144 ping-pong balls. More than half...Ch. 2.2 - Find E(X) for each of the distributions given in...Ch. 2.2 - Let the random variable X have the pmf...Ch. 2.2 - Let X be a discrete random variable with the...Ch. 2.2 - Prob. 4ECh. 2.2 - Let the random variable X be the number of days...Ch. 2.2 - Let the pmf of X be defined by...Ch. 2.2 - In Example 2.2-1 let Z=u(X)=X3. (a) Find the pmf...Ch. 2.2 - Let X be a random variable with support...Ch. 2.2 - In the gambling game chuck-a-luck, for a $1 bet it...Ch. 2.2 - In the casino game called high—low, there are...Ch. 2.2 - A roulette wheel used in an American casino has 38...Ch. 2.2 - Suppose that a school has 20 classes: 16 with 25...Ch. 2.2 - In the gambling game craps (see Exercise 1.3-13),...Ch. 2.3 - Find the mean, variance, and index of skewness for...Ch. 2.3 - For each of the following distributions, find...Ch. 2.3 - If the pmf of X is given by f(x), (I) depict the...Ch. 2.3 - Let and 2 denote the mean and variance of the...Ch. 2.3 - Consider an experiment that consists of selecting...Ch. 2.3 - Place eight chips in a bowl: Three have the number...Ch. 2.3 - Let X equal an integer selected at random from the...Ch. 2.3 - Let X equal the larger outcome when two fair...Ch. 2.3 - A warranty is written on a product worth $10,000...Ch. 2.3 - Let X be a discrete random variable with pmf...Ch. 2.3 - If the moment-generating function of X is...Ch. 2.3 - Let X equal the number of people selected at...Ch. 2.3 - For each question on a multiple-choice test, there...Ch. 2.3 - The probability that a machine produces a...Ch. 2.3 - Apples are packaged automatically in 3-pound bags....Ch. 2.3 - Let X equal the number of flips of a fair coin...Ch. 2.3 - Let X equal the number of flips of a fair coin...Ch. 2.3 - Let X have a geometric distribution. Show that...Ch. 2.3 - Given a random permutation of the integers in the...Ch. 2.3 - Construct a sequence of squares in the first...Ch. 2.4 - An urn contains seven red and 11 white balls. Draw...Ch. 2.4 - Suppose that in Exercise 2.4-1, X = 1 if a red...Ch. 2.4 - On a six-question multiple-choice test there are...Ch. 2.4 - It is claimed that 15% of the ducks in a...Ch. 2.4 - In a lab experiment involving inorganic syntheses...Ch. 2.4 - It is believed that approximately 75% of American...Ch. 2.4 - Suppose that 2000 points are selected...Ch. 2.4 - A boiler has four relief valves. The probability...Ch. 2.4 - Suppose that the percentage of American drivers...Ch. 2.4 - A certain type of mint has a label weight of 20.4...Ch. 2.4 - Find the index of skewness for the b(n,p)...Ch. 2.4 - In the casino game chuck-a-luck, three fair six-...Ch. 2.4 - It is claimed that for a particular lottery, 110...Ch. 2.4 - For the lottery described in Exercise 2.4-13, find...Ch. 2.4 - A hospital obtains 40% of its flu vaccine from...Ch. 2.4 - A company starts a fund of M dollars from which it...Ch. 2.4 - Your stockbroker is free to take your calls about...Ch. 2.4 - In group testing for a certain disease, a blood...Ch. 2.4 - Define the pmf and give the values of ,2, and ...Ch. 2.4 - Prob. 20ECh. 2.5 - In a lot (collection) of 100 light bulbs, there...Ch. 2.5 - On Wednesday afternoons, eight men play tennis on...Ch. 2.5 - A professor gave her students six essay questions...Ch. 2.5 - When a customer buys a product at a supermarket,...Ch. 2.5 - Five cards are selected at random without...Ch. 2.5 - To find the variance of a hyper geometric random...Ch. 2.5 - In the Michigan lottery game, LOT 10 47, the state...Ch. 2.5 - Forty-four states. Washington D.C., and the Virgin...Ch. 2.5 - Suppose there are three defective items in a lot...Ch. 2.5 - Prob. 10ECh. 2.5 - A Bingo card has 25 squares with numbers on 24 of...Ch. 2.6 - An excellent free-throw shooter attempts several...Ch. 2.6 - Show that 63512 is the probability that the fifth...Ch. 2.6 - Suppose that a basketball player different from...Ch. 2.6 - Suppose an airport metal detector catches a person...Ch. 2.6 - Let the moment-generating function M(t) of X exist...Ch. 2.6 - Use the result of Exercise 2.6-5 to find the mean...Ch. 2.6 - If E(Xr)=5r,r=1,2,3.... find the moment-generating...Ch. 2.6 - The probability that a companys workforce has no...Ch. 2.6 - One of four different prizes was randomly put into...Ch. 2.6 - In 2016, Red Rose tea randomly began placing one...Ch. 2.7 - Let X have a Poisson distribution with a mean of...Ch. 2.7 - Let X have a Poisson distribution with a variance...Ch. 2.7 - Customers arrive at a travel agency at a mean rate...Ch. 2.7 - If X has a Poisson distribution such that...Ch. 2.7 - Flaws in a certain type of drapery material appear...Ch. 2.7 - Find the index of skewness of a Poisson...Ch. 2.7 - With probability 0.001, a prize of $499 is won in...Ch. 2.7 - Suppose that the probability of suffering a side...Ch. 2.7 - A store selling newspapers orders only n = 4 of a...Ch. 2.7 - The mean of a Poisson random variable X is =9....Ch. 2.7 - An airline always overbooks if possible. A...Ch. 2.7 - A baseball team loses $100,000 for each...Ch. 2.7 - Assume that a policyholder is four times more...

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