Question: The density function of a random variable X is given by f (x) = c e|x| , < x < , for a

The density function of a random variable X is given by f (x) = c ⋅ e−|x|

, −∞ < x < ∞, for a real constant c.

(i) Find the value of c and draw the graphs of the density function and the distribution function of the variable X.

(ii) Obtain the expectation ???? = E(X) and the variance Var(X).

(iii) Calculate the following moments of order three for the variable X:

E[X3], E[|X|3], E[(X − ????)3].

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