TEAM PROJECT. Means, Variances, Expectations. (a) Show
Chapter 24, Problem 24.6(choose chapter or problem)
TEAM PROJECT. Means, Variances, Expectations. (a) Show that E(X - IL) = 0, (]"2 = E(X2) - IL2. (b) Prove (10)-(12). (c) Find all the moments of the uniform distribution on an interval a ~ x ~ b. (d) The skewness 'Y of a random variable X is defined by (13) 1 3 'Y = 3 E([X - ILl ). (]" Show that for a symmetric distribution (whose third central moment exists) the skewness is 7ero. (e) Find the skewness of the distribution with density fIx) = xe- x when x > 0 and fIx) = 0 otherwise. Sketch f(x). (I) Calculate the skewness of a few simple discrete distributions of your own choice. (g) Find a non symmetric discrete distribution with 3 possible values. mean O. and skewness O.
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