Mathematical Statistics and Data Analysis
3rd Edition
ISBN: 9781111793715
Author: John A. Rice
Publisher: Cengage Learning
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Chapter 2.5, Problem 34P
To determine
Prove that f is a density.
Compute the cumulative density
Compute the
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Chapter 2 Solutions
Mathematical Statistics and Data Analysis
Ch. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10P
Ch. 2.5 - Prob. 11PCh. 2.5 - Prob. 12PCh. 2.5 - Prob. 13PCh. 2.5 - Prob. 14PCh. 2.5 - Prob. 15PCh. 2.5 - Prob. 17PCh. 2.5 - Prob. 18PCh. 2.5 - Prob. 19PCh. 2.5 - Prob. 20PCh. 2.5 - Prob. 21PCh. 2.5 - Prob. 22PCh. 2.5 - Prob. 23PCh. 2.5 - Prob. 24PCh. 2.5 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.5 - Prob. 28PCh. 2.5 - Prob. 29PCh. 2.5 - Prob. 30PCh. 2.5 - Prob. 31PCh. 2.5 - Prob. 32PCh. 2.5 - Prob. 33PCh. 2.5 - Prob. 34PCh. 2.5 - Prob. 35PCh. 2.5 - Prob. 36PCh. 2.5 - Prob. 37PCh. 2.5 - Prob. 38PCh. 2.5 - Prob. 39PCh. 2.5 - Prob. 40PCh. 2.5 - Prob. 41PCh. 2.5 - Prob. 42PCh. 2.5 - Prob. 43PCh. 2.5 - Prob. 44PCh. 2.5 - Prob. 45PCh. 2.5 - Prob. 46PCh. 2.5 - Prob. 47PCh. 2.5 - Prob. 48PCh. 2.5 - Prob. 49PCh. 2.5 - Prob. 50PCh. 2.5 - Prob. 51PCh. 2.5 - Prob. 52PCh. 2.5 - Prob. 53PCh. 2.5 - Prob. 54PCh. 2.5 - Prob. 55PCh. 2.5 - Prob. 56PCh. 2.5 - Prob. 57PCh. 2.5 - Prob. 58PCh. 2.5 - Prob. 59PCh. 2.5 - Prob. 60PCh. 2.5 - Prob. 61PCh. 2.5 - Prob. 62PCh. 2.5 - Prob. 63PCh. 2.5 - Prob. 64PCh. 2.5 - Prob. 65PCh. 2.5 - Prob. 66PCh. 2.5 - Prob. 67PCh. 2.5 - Prob. 68PCh. 2.5 - Prob. 69PCh. 2.5 - Prob. 70P
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Given the density function
f(x) = 2(1 − x), for 0 < x < 1,
= 0, otherwise.
Find the standard deviation
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Suppose that X and Y have a joint probability density function
f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise.
(a) Compute P(X + Y less than or equal 1).
(b) Find the marginal probability density functions for X and Y , respectively.
(c) Are X and Y independent?
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let X and Y are two random variables with p.d.f as f(x,y)=3x2y+3yx2 0<x<1 0<x<1.find conditional density of X given Y?.Find mean mode and standard deviation of r.v Y?. Correlation between X and Y?. check that X and Y are independent or not?.
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If the probability density of X is given by
f(x) =kx3(1 + 2x)6 for x > 00 elsewhere
where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X
1 + 2X . Identify thedistribution of Y, and thus determine the value of k.
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Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.
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Suppose that the random variables X and Y have a joint density function given by:
f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise
P(3 < X < 5, Y >1),
P(X < 3),
P(X +Y > 5),
Find the joint distribution function (cdf),
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Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density
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If X has the uniform density with the parameters α = 0and β = 1, use the distribution function technique to findthe probability density of the random variable Y = √X.
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Given the cumaltive distribution function F(x) = x3 for 0<x<1, determine the probabilty density function, f(x). Make sure to indicate all possible values of x from negative infinity to infinity.
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Let the continuous random variable X denote the current measured in a thin copper wire in milliamperes. Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X is f(x) = 5 for 4.9 <= x <= 5.1. What is the variance?
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For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function
fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value.
(a) Find the marginal density fX(x) for the total amount of time spent at the clinic.
(b) Find the conditional density for waiting time, given the total time.
(c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes.
(Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
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For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is f(x) = 2x(1-x), 0 < x < 1
Find the variance and standard deviation of X
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