Answer Happy

Impurities in batches of product of a chemical process reflect a serious problem. It is known that the proportion of impurities Y in a batch has the following density function. Complete parts (a) through (e) below. f(y) = 9(1-y), osys1, 0, elsewhere (a) Verify that the given function is a valid density function. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. O A. The given function is a valid density function because I 9(1 - y)®dy = 0 OB. The given function is a valid density function because it is at least 0 everywhere. OC. The given function is a valid density function because it is at least O everywhere and because I 9(1 - yje dy = 1. 0 (b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. What is the probability that a batch is considered not acceptable (i.e., Y>0.6)? The probability is (Round to four decimal places as needed.) (c) What are the parameters a and ß of the beta distribution illustrated here? (Y (Type an integer or a decimal. Do not round.) (Type an integer or a decimal. Do not round.) OX (d) The mean of the beta distribution is What is the mean proportion of impurities in the batch? Q+B u= (Round to four decimal places as needed.) (e) The variance of a beta distributed random variable is 62 αβ (a + b)2(a +B+1) What is the variance of Y in this problem? o? =D (Round to six decimal places as needed.)