Consider the density function of a random variable X defined by

(a) Find the CDF corresponding to this density function. (Be sure you describe it completely.)
(b) Calculate the mean and variance.
(c) What is the probability that a random variable having this density will exceed 0.5?
(d) Consider the experiment where six independent random variables are observed, each random variable having the density function given above. What is the expected value of the sample mean of these observations?
(e) What is the variance of the sample mean described in part (d)?

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