# Question

(a) If the probability density of X is given by

Find E(X), E(X2), and E(X3).

(b) Use the results of part (a) to determine E( X3 + 2X2 - 3X + 1).

Find E(X), E(X2), and E(X3).

(b) Use the results of part (a) to determine E( X3 + 2X2 - 3X + 1).

## Answer to relevant Questions

With reference to Exercise 3.47 on page 90, find E(2X – Y). Find µ, µ'2, and σ2 for the random variable X that has the probability density The symmetry or skewness (lack of symmetry) of a distribution is often measured by means of the quantity α3 = µ3/σ3 Use the formula for µ3 obtained in Exercise 4.25 to determine α3 for each of the following ...If we let RX(t) = lnMX(t), show that R'X(0) = µ and R''X(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment- generating function MX(t) = e4(e4 – 1) If X and Y have the joint probability distribution f(–1, 0) = 0, f(–1, 1) = 14 , f(0, 0) = 16 , f(0, 1) = 0, f(1, 0) = 1 12 , and f(1, 1) = 12 , show that (a) cov(X, Y) = 0; (b) The two random variables are not ...Post your question

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