A machine makes a product that is screened (inspected 100 percent) before being shipped. The measuring...

 

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A machine makes a product that is screened (inspected 100 percent) before being shipped. The measuring instrument is such that it is difficult to read between 1 and '3 (coded data). After the screening process takes place, the measured dimension has density kz2 for 0 <z <1 for 1 < z <1 f(2) = {1 otherwise (a) Find the value of k. (b) What fraction of the items will fall outside the twilight zone (fall between 0 and 1)? (C) Find the mean and variance of this random variable. A machine makes a product that is screened (inspected 100 percent) before being shipped. The measuring instrument is such that it is difficult to read between 1 and '3 (coded data). After the screening process takes place, the measured dimension has density kz2 for 0 <z <1 for 1 < z <1 f(2) = {1 otherwise (a) Find the value of k. (b) What fraction of the items will fall outside the twilight zone (fall between 0 and 1)? (C) Find the mean and variance of this random variable.

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