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The random variable X has the following density function f(x) = ( c(1 + x 2...

The random variable X has the following density function f(x) = ( c(1 + x 2 ) if 0 < x < 1 0 if otherwise a./ Find the value of c. b./ Find E(X). c./ Suppose that the random variable X represents the lifetime of a water filter (of a refrigerator) measured in years. What is the probability that a randomly selected filter will live more than half a year. d./ If a restaurant orders 6 such filters for their refrigerators what is the probability that at least 5 will live more than half a year.

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