Series expansion method of the mgf

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Reference no: EM13243054

The continuous random variable X has probability density function (pdf) given by

                                            493_Measure of skewness in the distribution1.png


Show that, subject to t < 1, the Moment Generator Function, MGF, of X is:

                                                        858_Measure of skewness in the distribution.png

 

Use the series expansion method of the MGF to find E(X), E(X2) and E(X3), the first three moments of X about the origin. Use your results to show that the mean and variance of X are both equal to 2.

The standardised third moment, b3 = E{ (X - m)3  ÷ s}, provides a measure of skewness in the distribution of X. Determine the value of b3 for this distribution.  
                          
Using a suitable distributional approximation, find the probability that the mean of a random sample of n = 25 observations will exceed 2.5.

Reference no: EM13243054

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