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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Chapter 3.2, Problem 10E
Use the moment-generating
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Chapter 3 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
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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- let the pdf f(x) is even function then E(x) is?arrow_forwardSketch the graphs of the beta densities having(a) α = 2 and β = 2;(b) α = 12 and β = 1;(c) α = 2 and β = 12 ;(d) α = 2 and β = 5.arrow_forwardGiven the pdf: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.arrow_forward
- The function f has a continuous derivative. The table below gives values off and its derivative at x = 0 and ƒ (x) dx = 8 x.f' (x) dx X = 4. If what is the value of X f (x) | ƒ '(x) 0 2 5 4 -3 11arrow_forward(part 1 of 4) Determine the value of the third derivative of f at x = 1 when f(x) 1. f"(1) 2. f" (1) 3. f(1) 4. f"(1) 5. f""(1) 1. T3 = =e 3. T3 = = = e 4. T3 e = e³ -1 -8 e³ (part 2 of 4) Determine the degree three Taylor polyno- mial centered at x = 1 for f when 3-4x f(x) 8 3! 3! e³ -3!8 e³ = 2. T3 =e7 (1 + 4(x − 1) e(5-2x) (1 - 4(x - 1) 32 + 8(x − 1)² — 33² (x − 1)²³) ¹(1. - 8(x − 1)² + 1-4x+8x² 1+ 4x − 8x² + 5. T3 =14(x − 1) 32 3²(x - 1)³) 32-2³) (3²-2-2) + 8(x − 1)² – 32 3 (x - 1)³arrow_forwardDetermine whether the given set of functions is linearly independent on the interval (-00, 00). fi (x) = e*, f2(x) = e-*, fg(x) = sinh(x) linearly dependent O linearly independentarrow_forward
- Find the derivative of the function.arrow_forwardFind the first and second derivatives of the function. f(x) = x/(7+x2) Identify the intervals on which it is concave up/down.arrow_forwardD5) Consider the logistic regression model P(Y=1) = 1 /( 1 + exp(-(a+bx))) where a = 1, b = 1.5 and the errors are normally distributed with mean 0 and standard deviation 1. Let x be a sequence from -4 to 4 in increments of 0.1. Estimate the bias of the slope for a simple linear regression model at x = 0 compared to the true slope (change in probability over change in x) of the logistic function at x = 0arrow_forward
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