Consider a random variable Y with densityS (1/2)(y + 1), -1 < y < 1,else.f(y)Calculate E(W) and V(W) for the random variable W = 4+Y – 2Y².

From the given information, f(x)=12(y+1), -1≤y≤1 Consider, E(y)=∫-11yf(y)dy =∫-11y*12(y+1)dy…

Answered: Consider a random variable Y with…

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Consider a random variable Y with density f(y) = { (1/2)(y + 1), -1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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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!

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Consider a random variable Y with density
S (1/2)(y + 1), -1 < y < 1,
else.
f(y)
Calculate E(W) and V(W) for the random variable W = 4+Y – 2Y².

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