2. A random variable X has a probability density function (pdf) given by 20<<1, f(1) = C, 1
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2. A random variable X has a probability density function (pdf) given by 20<<1, f(1) = C, 1
2. A random variable X has a probability density function (pdf) given by 20<<1, f(1) = C, 1<x<3, 0, elsewhere, for some real constant c. (a) Determine the value of the constant c and sketch the graph of f(x). In the following questions, replace c by its numerical value computed in (a). (b) Find the cumulative distribution function (cdf) F(t) of X, and sketch its graph. (C) Find P(X < ). (d) Find P < X < $). (e) What is P(X = 1)? (f) Find the moment-generating function (mgf) Mx(t) of X. Justify why it is well defined for any real finite value of t.
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