• A random variable X that has the characteristic function as shown below.Px(w) = (1– j2w)-212) Find the mean value of X.13) Find the variance of X.14) Find the skewness of X given that m, = 192.X is an exponential random such that fx(x) = e. If the linear random variabletransformation is made such that Y = 3X + 10.15) Find the PDF of Y fy0).16) Find the mean of Y.

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• A random variable X that has the characteristic function as shown below. Ox(w) = (1– j2w)-2 12) Find the mean value of X. 13) Find the variance of X. 14) Find the skewness of X given that m, = 192.

• A random variable X that has the characteristic function as shown below. Ox(w) = (1– j2w)-2 12) Find the mean value of X. 13) Find the variance of X. 14) Find the skewness of X given that m, = 192.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

• A random variable X that has the characteristic function as shown below.
Px(w) = (1– j2w)-2
12) Find the mean value of X.
13) Find the variance of X.
14) Find the skewness of X given that m, = 192.
X is an exponential random such that fx(x) = e. If the linear random variable
transformation is made such that Y = 3X + 10.
15) Find the PDF of Y fy0).
16) Find the mean of Y.

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