Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 16.2, Problem 2E
Define each of the following:
- a Prior distribution for a parameter θ
- b Posterior distribution for a parameter θ
- c Conjugate prior distribution
- d Bayes estimator for a
function of θ, t(θ)
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Let X - U[0, 1]. Find the distribution of Y = 1 - X.
Question 2
A random variable X has a probability density function
0; x<0,
f(x) = { 0≤x≤1,
; 1
Suppose that X and Y have following joint probability distribution:
F(x,y)
X
2
1
0.10
y
3
0.20
5
0.10
a.) Find the marginal distribution of X.
b.) Find the marginal distribution of Y.
LO
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0.15
Chapter 16 Solutions
Mathematical Statistics with Applications
Ch. 16.2 - Refer to the results of Example 16.2 given in...Ch. 16.2 - Define each of the following: a Prior distribution...Ch. 16.2 - Suppose that Y is a binomial random variable based...Ch. 16.2 - In Section 16.1 and Exercise 16.6, we considered...Ch. 16.2 - Refer to Exercise 16.6. If Y is a binomial random...Ch. 16.2 - Suppose that we conduct independent Bernoulli...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forward1Example 23. A distribution x1, X2,..., Xp., Xp with frequencies, fp f2,..., f..., fn is transformed into the distribution y1, y2,.….., Y,.., yn with the same corresponding frequencies by the relation y, = ax, + b, where a and b are constants. Show that the mean, median and mode of the new distribution are given in terms of the first distribution by the same transformation.arrow_forwardUse what you know about order statistics to show that for the random sample of size n = 3 the median is an unbiased estimator of the parameter θ of a uniform population with α = θ − 1/2 and β = θ + 1/2.arrow_forward
- Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 2, 3. c. List the cumulative distribution function F(x). x f(x, y) 1 2 3 0.10 1 0.05 0.05 3 0.05 0.10 0.35 Y 5 0.00 0.20 0.10arrow_forwardLet X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3 b. Find the marginal distribution h(y), y = 1, 2, 3. c. List the cumulative distribution function F(x).arrow_forwardLet x = (x1.X2 .. .x,. . ,,) be a data set with a sample mean x. Show that E(x, – x) = 0.arrow_forward
- Let X denote the number of times a certain numericalcontrol machine will malfunction: 1, 2, or 3times on any given day. Let Y denote the number oftimes a technician is called on an emergency call. Theirjoint probability distribution is given below: a.Find the marginal distributiong(x), x= 1, 2, 3.b.Find the marginal distributionh(y), y= 1, 2, 3.c.List thecumulativedistribution function F(x).d.List thecumulativedistribution function F(y).e.Find the conditional distribution of f(x|y), P(X = 1 | Y = 3).f.Find the conditional distribution of f(y|x), P(X = 3| Y = 3).g.Determine if the random variables are statistically independentconsidering f(2, 1).arrow_forwardLet X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below:a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 3, 5. c. List the cumulative distribution function F(x). d. List the cumulative distribution function F(y). e. Find the conditional distribution of f (x|y), P(X = 1 | Y = 3).f. Find the conditional distribution of f (y|x), P(X = 3 | Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1).arrow_forwardFor a t-curve with df=9, use a t-distribution table to find the t-value t0.025. t0.025=_____________ (Type an integer or a decimal.)arrow_forward
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