Example 4.1.8 A continuous distribution is given by the density function1f (x) =e-(12X log x)²xV2nfor x > 0for x < 0Find the mean, mode and standard deviation of the distribution.

Given: f(x)=1x2πe-12logx2 for x>0 =0 for x<0

Answered: Find the mean, mode and standard…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
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Example 4.1.6(a) Find the median and mode of a distribution having the density function de- (x> > 0).
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Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.
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3. The lifetime in hours of an electronic gadget is a random variable having a probability density function of f(x) = xe-2x x 2 0. Compute the variance and the standard deviation.
Let the continuous random variable X denote the distance in micrometers from the start of a track on a magnetic disk until the first flaw. Historical data show that the distribution of X can be modeled by a pdf: 1 f (x) = x > 0 e 2000 2000 For what proportion of disks is the distance to the first flaw greater than 1,418 micrometers?
Variable x has a uniform distribution with values between 5 and 15 being equally likely. Variable y has a Pareto distribution. A Gaussian copula is used to define the correlation between the two distributions. A Gaussian copula is used to define the correlation between the two distributions. The Pareto distribution for variable y has a probability density function aca/ya +1 for values of y between c and infinity where c = 4 and a = 0.5. Produce a table similar to Table 9.5 in the text considering values of x equal to 7, 9, 11, and 13 and values of y equal to 5, 10, 30, and 60. Assume a copula correlation of 0.4.
5. Given a normalized probability density function P(x) of finding the variable x in the interval [x,x + dx], write the definition for a) the mean value (x), b) the variance o? = ((x – (x))?), and c) the standard deviation of the variable x.
Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.
Question 4: The density function of a continuous random variable X is [4x(9-x)/81 0sxs3 1o f(x) = otherwise (a) Find the mode, (b) Find the median. (c) Compare mode, median, and mean. %3D Question 5: %3D A test engineer discovered that the cumulative distribution fuction of the ifetime of an n Vatislc.expectedlifetime of the

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