Impurities in batches of product of a chemical process reed 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. 12(1y)\". \"t I], elsewhere vl= (a) I|v'en'fy that the given function is a valid density function. Select the correct choice below and, it necessary, ll in the answer boxes within your choice. 1 O A. The given function is a valid density function because it is at least 0 everywhere and because 112(1 y]11 dy = D. o O B_ The given function is a valid density function because it is at least 0 everywhere. 1 O C. The given function is a valid density function because I12\" y)\"cly = D (b}Abatch is considered not sellable and then not acceptable if the percentage of impurities exceeds 55%. What is the probability that a batch is considered not acceptable {i.e., Y > 0.55}? The probability is . (Round to four decimal places as needed.) (c) What are the para meters at and [3 of the beta distribution illustrated here? a = (Type an integer or a decimal. Do not round.) : (Type an integer or a decimal. Do not round.) I] (d) The mean of the beta distribution is f' What is the mean proportion of impurities in the batch? p = (Round to four decimal places as needed.) 11B (e) The variance of a beta distributed random valiable is 02 = 2 {II-t) [a++1} 02=D (Round to six decimal places as needed.) . What is the variance on in this problem?