1. Let X be a
   continuous random variable with probability density function
   (pdf)

   ()

   (a) Evaluate the constant so
   that ( )
   is a proper pdf. Then, find the
   cumulative distribution function (cdf) of X.

   (b) Determine the probability
   that X takes a value between 0.1 and 0.5. (c) Find the
   median, the mean and the variance of X.

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