2. Some properties of Expected value and variance of a random variable.a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definiticShow:andE(aX + b) = a · E(X) + bV(aX + b) = a² · V(X )Stat 3128 Ali MahzarniaPSTAT 3128Ali Mahzarniab) Justify the computational formula of Variance of a random variable which is to justify :V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2:Here needsjustificationBy Cauchy Schwarz inequality it can be shown that the right hand side is always positive.Analogs expression in Mechanic : Parallel axis theoremIem= I– md²Moment ofMoment ofinetria aboutInertia of anan axis shiftedobject about thecenter of a massby d fromcenter of mass(a parallel shift)Icm is dispersion around the mean and is like second central moment(variance) I is like second moment if d is meanm is like sum total all the weight of each of the x which all add up to 1d squared is like squared of mean since we,

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Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Er– µ}° • ptx) = | Ex² - px) – µ² = E(X*) – [EX)F Σ Here needs justification

Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Er– µ}° • ptx) = | Ex² - px) – µ² = E(X*) – [EX)F Σ Here needs justification

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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