MATH 431 Final: 2011 Math 431 - Seppalainen - Spring Final
Document Summary
431 introduction to the theory of probability spring 2011. 1. (10 pts) let a and b be events in a sample space with probabilities p (a) = 1/2 and. Find the density of y . (this random variable y is called lognormal. ) 3. (15 pts) suppose 0. 25 percent of households earn over 450,000 a year. A random sam- ple of 400 households has been chosen. In this sample, let y be the number of households that earn over 450,000. Find a simple estimate for the probability p (y 2). X1, x2, x3, . are the lifetimes of the successive lightbulbs, assumed independent and each xk exponentially distributed with parameter . The number of lightbulbs in the box is n . N is ran- dom, independent of the xk"s, and has geometric distribution with parameter p. the total random time that this box of bulbs lasts is the sum s = pn k=1 xk. Let sn = x1 + + xn.
