Impurities in batches of product of a chemical process reect a serious problem. It is known that the proportion of impurities X in a batch has the density function _ 10(1x)9, 05x51 f(x) _ { 0, else 4. (4 points) Verify that the above is a valid density function. 5. (4 points) What is the probability that the proportion of impurities in a batch exceeds 0.6? 6. (4 points) What is the mean proportion of impurities in the batch