Mathematical Statistics and Data Analysis
3rd Edition
ISBN: 9781111793715
Author: John A. Rice
Publisher: Cengage Learning
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Chapter 2.5, Problem 67P
a.
To determine
Obtain the density
b.
To determine
Verify that
c.
To determine
Explain how Weibull random variables can be generated from a uniform random number generator.
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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.)
Calculate the E(X) when the joint probability density function of X and Y is fxy(X,Y)=c(X+Y) over the range x = 1, ..., 4 and y = 1, ..., 2
The PDF of a continuous random variable X is as follows:
f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to)
a. For this to be a proper density function, what must be the value of c ?
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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