2. A random variable X has a probability density function (pdf) given by 글, 0

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2. A random variable X has a probability density function (pdf) given by
, 0< x < 1,
f(x) =
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(x) of X, and sketch its graph.
(c) Find P(X < ).
(d) Find P( < X < ).
Transcribed Image Text:2. A random variable X has a probability density function (pdf) given by , 0< x < 1, f(x) = 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(x) of X, and sketch its graph. (c) Find P(X < ). (d) Find P( < X < ).
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