Probability and Statistical Inference (9th Edition)

9th Edition

ISBN: 9780321923271

Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Publisher: PEARSON

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

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The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

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Textbook Question

Chapter 3.3, Problem 2E

If Z is N ( 0 , 1 ) , find

(a) P ( 0 ≤ Z ≤ 0.78 ) .

(b) P ( − 2.46 ≤ Z ≤ 0 ) .

(d) P ( | Z | > 1.93 ) .

(e) P ( Z < − 1.26 ) .

(f) P ( | Z | > 1 ) .

(g) P ( | Z | > 2 ) .

(h) P ( | Z | > 3 ) .

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Chapter 3.3, Problem 1E

Chapter 3.3, Problem 3E

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Chapter 3 Solutions

Probability and Statistical Inference (9th Edition)

Ch. 3.1 - Show that the mean, variance, and mgf of the...Ch. 3.1 - Let X be a continuous random variable with pdf...Ch. 3.1 - Customers arrive randomly at a bank tellers...Ch. 3.1 - If the mgf of X is M(t)=e5te4tt,t0andM(0)=1,, find...Ch. 3.1 - Let Y have a uniform distribution U(0,1), and let...Ch. 3.1 - A grocery store can order n watermelons from a...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - Prob. 9E Ch. 3.1 - The pdf of X is f(x)=cx2,1x. (a) Calculate the...

Ch. 3.1 - The pdf of Y is g(y)=cy3,1y. (a) Calculate the...Ch. 3.1 - Sketch the graphs of the following pdfs and find...Ch. 3.1 - The logistic distribution is associated with the...Ch. 3.1 - Find the variances of each of the distributions...Ch. 3.1 - The life X (in years) of a voltage regulator of a...Ch. 3.1 - Let f(x)=(x+1)2,1x1. Find (a) 0.64, (b) q1=0.25,...Ch. 3.1 - An insurance agent receives a bonus if the loss...Ch. 3.1 - Prob. 18E Ch. 3.1 - The total amount of medical claims (in $100000) of...Ch. 3.1 - Nicol (see References) lets the pdf of X be...Ch. 3.1 - Let X1,X2,...,Xk be random variables of the...Ch. 3.2 - Prob. 1E Ch. 3.2 - Telephone calls arrive at a doctors office...Ch. 3.2 - Let X have an exponential distribution with mean...Ch. 3.2 - Let F(x) be the cdf of the continuous-type random...Ch. 3.2 - There are times when a shifted exponential model...Ch. 3.2 - A certain type of aluminum screen 2 feet in width...Ch. 3.2 - Find the moment-generating function for the gamma...Ch. 3.2 - If X has a gamma distribution with =4 and =2, find...Ch. 3.2 - If the moment-generating function of a random...Ch. 3.2 - Use the moment-generating function of a gamma...Ch. 3.2 - Let X have a gamma distribution with parameters ...Ch. 3.2 - Let X equal the number of alpha particle emissions...Ch. 3.2 - If X is x2(23), find the following: (a)...Ch. 3.2 - If X is x2(12), find constants a and b such that...Ch. 3.2 - Prob. 15E Ch. 3.2 - Cars arrive at a tollbooth at a mean rate of five...Ch. 3.2 - If 15 observations are taken independently from a...Ch. 3.2 - Say the serum cholesterol level (X) of U.S. males...Ch. 3.2 - A bakery sells rolls in units of a dozen. The...Ch. 3.2 - The initial value of an appliance is $700 and its...Ch. 3.2 - A loss (in $100000) due to fire in a building has...Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.3 - If Z is N(0,1), find (a) P(0.47Z2.13). (b)...Ch. 3.3 - If Z is N(0,1), find (a) P(0Z0.78). (b) P(2.46Z0)....Ch. 3.3 - If Z is N(0,1), find values of c such that (a)...Ch. 3.3 - Find the values of (a) z0.10, (b) z0.05, (c)...Ch. 3.3 - If X is normally distributed with a mean of 6 and...Ch. 3.3 - If the moment-generating function of X is...Ch. 3.3 - If X is N(650,400), find (a) P(600X660). (b) A...Ch. 3.3 - Prob. 8E Ch. 3.3 - Find the distribution of W=X2 when (a) X is...Ch. 3.3 - If X is N(,2) show that Y=aX+b is N(a,+b,a22),a0,...Ch. 3.3 - A candy maker produces mints that have a label...Ch. 3.3 - Prob. 12E Ch. 3.3 - The serum zinc level X in micrograms per deciliter...Ch. 3.3 - The strength X of a certain material is such that...Ch. 3.3 - The fill problem is important in many industries,...Ch. 3.3 - The graphs of the moment-generating functions of...Ch. 3.3 - Prob. 17E Ch. 3.4 - Let the life W (in years) of the usual family car...Ch. 3.4 - Suppose that the length W of a mans life does...Ch. 3.4 - Let Y1 be the smallest observation of three...Ch. 3.4 - Prob. 4E Ch. 3.4 - Let X be a random variable of the mixed type...Ch. 3.4 - Let X be a random variable of the mixed type...Ch. 3.4 - Prob. 7E Ch. 3.4 - Find the mean and variance of X if the cdf of X is...Ch. 3.4 - Consider the following game: A fair die is rolled....Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Let X have an exponential distribution with =1;...Ch. 3.4 - A loss X on a car has a mixed distribution with...Ch. 3.4 - A customer buys a $1000 deductible policy on her...Ch. 3.4 - A certain machine has a life X that has an...Ch. 3.4 - Prob. 16E Ch. 3.4 - Some banks now compound daily, but report only on...Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Let X be the failure time (in months) of a certain...Ch. 3.4 - In a medical experiment, a rat has been exposed to...

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If Z is N ( 0 , 1 ) , find (a) P ( 0 ≤ Z ≤ 0.78 ) . (b) P ( − 2.46 ≤ Z ≤ 0 ) . (c) P ( − 2.31 ≤ Z ≤ − 0.65 ) . (d) P ( | Z | &gt; 1.93 ) . (e) P ( Z &lt; − 1.26 ) . (f) P ( | Z | &gt; 1 ) . (g) P ( | Z | &gt; 2 ) . (h) P ( | Z | &gt; 3 ) .

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Chapter 3 Solutions

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If Z is N ( 0 , 1 ) , find (a) P ( 0 ≤ Z ≤ 0.78 ) . (b) P ( − 2.46 ≤ Z ≤ 0 ) . (c) P ( − 2.31 ≤ Z ≤ − 0.65 ) . (d) P ( | Z | > 1.93 ) . (e) P ( Z < − 1.26 ) . (f) P ( | Z | > 1 ) . (g) P ( | Z | > 2 ) . (h) P ( | Z | > 3 ) .