Exams Fall 2015-AMAT554-Intro to Theory of Statistic IExams Fall 2015-AMAT554-Intro to Theory of Statistic I

• 1. An insurance company insures a large number of homes. The insured value, X, of a randomly selected home is assumed to follow a distribution with density function f(x)=4x^-5 , for x>1. Given that a randomly selected home is insured for at least 2, what is the probability that it is insured for less than 4?

• 2. Let X be uniform on [-1,3]. Find the pdf of Y=X². Be careful. Separate the cases 0 y 1 and y > 1. Specify the range of values for Y. Make a picture