Question

1) The probability density function of the diameter (in micrometers) of a particular type of contaminant particle can be modeled by f(x) = (x3 Exp(-x/2)]/96, x 20 a) Plot the pdf and the CDF of these diameters b) Compute E(Diameter) y Var(Diameter) c) Compute Pr(Diameter > 4), Pr(Diameter > 8), and Pr(Diameter > 12), d) Assume that the following random sample of 100 diameters of these particles has been taken. What is the probability that sample average if greater than 8.5 micrometers? e) An engineer, graduated from a university in SI. states that he took a random sample of 500 particle diameters and the average particle diameter the he computed is 8.5 micrometers. Do you believe his claim? Why? Why not?

Answer 1

solution : - a) palp plot of Doe te gaan met het geë nefti b) ECX) = face mappe en 1:1-8 ECR)- Je my pełda = 80 Nad(x) = E(XP) - E(X)*2= 8 -888 = 16 e) P (834) Elle et de la (pecimee :0.85712 --.) P (38) as (Decimal : 0.4334-7---) De 96 p(9512): the eventuele en Corcinox : 0.156.-. d) p (x bad >8.5) =p120(8.5-8) / sqot (16/100)] EP (2>las) T= 0.1056) Scanned with CamScanner