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A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 +...

A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 + e−x ) −1 , −∞ < x < ∞.

(i) Find the probability density function (pdf) of X.

(ii) Roughly, take 10 points in the range of x (5 points below 0 and 5 points more than 0) and plot the pdf on these 10 points. Does it look like the pdf is symmetric around 0?

(iii) Also, find the expected value of X.

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