Question: 5.79 The random variable X has probability density function as follows: f1x2 = x for 0 6 x 6 1 2 - x for

5.79 The random variable X has probability density function as follows:

f1x2 = •

x for 0 6 x 6 1 2 - x for 1 6 x 6 2 0 for all other values of x

a. Graph the probability density function for X.

b. Show that the density has the properties of a proper probability density function.

c. Find the probability that X takes a value between 0.5 and 1.5.

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