answer these problems

Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = 10. elsewhere. (a) Determine * that renders f(x) a valid density function.(b) Find the probability that a random error in measurement is less than 1/2. (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., (x]) exceeds 0.8. What is the probability that this occurs? Five independent coin tosses result in HHHHH. It turns out that if the coin is fair the probability of this outcome is (1/2)5 = 0.03125. Does this produce strong evidence that the coin is not fair? Comment and use the concept of P-value discussed inSection 1.1.For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 s X