Answer Happy

141 Question 11: Suppose that = {HHHHHT, HTT,ITT), 4 = 2" and (4) · New, let Yhe a random 111 for w = HHH variable on the probability space [1,4,P] defined by: X(a) = 1 for a = - ННТ, HTT for @= TTT 17 Then: a) Represent this random variable graphical. 2 2 09- 0.5-1 0.7- 0.6 03H 0.1- 03 02+ 0.1+ - 3 for I<-3 for-3511 for 1 SI<2 for 122 b) Determine the event in the relation: { W2;X() ) = c) Determine the distribution function Fy and sketch it. 0.9- 0.8 0.7- 0.6- 05- 0.44 03- 0.2+ 0.1 + F(x) = Question 13: A factory produce a kind of light bulbs. It claims by 95% confidence level, that the mean lifetime of the lamps has 41 = 500 hours working with standard deviation o = 5 working hours. We select a sample of 36 bulbs and find that the mean lifetime of the lamps equal to 480 hours working. Then: a) Determine 95% confidence interval for the mean lifetime. (The standard normal distribution table is on the next page). b) If the sample size equal to 100, what is the value for the margin error ? c) If the margin error 8 = 0.15 (for the 95% confidence level), what is the sample size which we use ?