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Unformatted text preview: M X ( t ), and use it to nd E( X ) and V( X ). STA 4321 - Introduction to Probability Theory Spring 2010 1 Jorge Roman STA 4321 4. The proportion of impurities per batch in a certain type of industrial chemical is a random variable X that has the probability density function f ( x ) = 20 x 3 (1-x ) when 0 x 1 and f ( x ) = 0 otherwise. (a) Find the c.d.f of X . (b) Suppose that a batch with a proportion of impurities over 30% cannot be sold. What is the probability that a randomly selected batch cannot be sold for this reason? (c) Find E( X ) and V( X ). [Hint: Is this p.d.f a special case of a known family of p.d.fs?] (d) Suppose that the dollar value of each batch is given by D = 10-. 75 X . Find E ( D ) and V ( D ). STA 4321 - Introduction to Probability Theory Spring 2010 2 Jorge Roman...
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