Probability And Statistical Inference (10th Edition)
10th Edition
ISBN: 9780135189399
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 3.3, Problem 1E
If Z is
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
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6.
Let X be a random variable taking values in (0,∞) with proba-
bility density function
fx(u) = 5e5u
u > 0.
Total marks 8
Let Y = X2. Find the probability density function of Y.
[8 Marks]
5.
Let a probability measure P on ([0,3], B([0,3])) be given by
1
dP(s):
=
½ s² ds.
9
Consider a random variable X : [0,3]
→ R given by
X(s) = s², sc [0,3].
S
Total marks 7
Find the distribution of X.
[7 Marks]
Problem: The probability density function of a random variable is given by the exponential
distribution
Find the probability that
f(x) = {0.55e−0.55x 0 < x, O elsewhere}
a. the time to observe a particle is more than 200 microseconds.
b. the time to observe a particle is less than 10 microseconds.
Chapter 3 Solutions
Probability And Statistical Inference (10th 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. 9ECh. 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. 18ECh. 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. 1ECh. 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. 15ECh. 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 - Find the index of skewness of the x2(r)...Ch. 3.2 - Some dental insurance policies cover the insurer...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. 8ECh. 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. 12ECh. 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. 17ECh. 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. 4ECh. 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. 7ECh. 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. 10ECh. 3.4 - Prob. 11ECh. 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. 16ECh. 3.4 - Some banks now compound daily, but report only on...Ch. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 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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