Example 5-15 Calculate the variance of g(X) = 2X +3, where X is a random variable withprobability distribution(2)|find the moon01/411/821/21.1Ov31/87

Answered: Example 5-15 Calculate the variance of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose a random variable X has expected value E[X] = -4 and variance Var(X) = 16. Compute the following quantities. (a) E[X-1] (b) E[X²] (c) E[(x - 1)²] (d) Var[3X + 2]
b) Suppose that a continuous random variable X is associated with the following function: (i) Show that c = =1/15 2 71 Page 0 < x < 2, Scx, f(x) = {0, elsewhere. lo, (ii) Calculate the mean and variance of X. (iii) Find the CDF of the random variable X, F(x). (iv) Use either the probability distribution function (pdf) of X, f(x), or the cumulative probab distribution function (cdf) of X, F(x), to compute P(0.25 < x < 1.25).
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ans Theorem 9.3. Let X and Y be independent random variables with finite variances, and a, b ER. Then Var(aX) = a²Var (X), Var (X+Y) = VarX + Var Y, Var (ax + bY) = a²VarX + b²Var Y. sercise Prove the theorem. Remark 9.2. Independence is sufficient for the variance of the sum to be equal to the sum of the variances, but not necessary. Remark 9.3. Linearity should not hold, since variance is a quadratic quantity. Remark 9.4. Note, in particular, that Var (-X) = Var(X). This is as expected, since switching the sign should not alter the spread of the distribution.
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Example 5-15 Calculate the variance of g(X) = 2X +3, where X is a random variable with probability distribution I f(x) 0 1/4 1 1/8 2 1/2 3 1/8