(10) Q3. A box contains two blue, three white and five red balls. A sample of six balls is drawn with replacement. What is the probability that (a) one is blue, two are white and three are red, (b) two of the each colour appears, (c) three are white, one is blue and three are red. (10) 04a) Find out the interval for the correlation coefficient of the two normal random variables. b) There are 3 coins, identical, one of which is ideal and the other 2 are biased with probabilities .333 and .667 respectively for a head. One coin is chosen at random and tossed twice. lfa head appears both the times, what is the probability that the biased coin was chosen? (10) Good Luck Basic Sciences Department Final Exams, Spring 2020 4'\" Semester (Software ling.) Course Title: Probability 8: Statistics Max. Time: 3 hrs. Max Marks: 40 NOTE: Attempt all the questions. Q1. Find the product moment coefficient of correlation for the regression lines X = 94.977 7 4.56617 (X on Y), and Y = 20.636 7 1.273X (Y on X) and X : 74.074 + 1.543Y (X on Y), and Y : 2.082 + 1.091X (Y on X). (10) 02a) Find the probability of getting between 6 and 9 heads inclusive in fifteen tosses of an ideal coin by the normal approximation to the binomial and the binomial distribution. b) The mean land the standard deviation of the students normally distributed, appearing for a test is 170 and 3.8. If thirty percent of the students considered as fail because of the lower marks then what are the minimum passing marks of the test for the students. Activate Windows 1% 3 to Settings to activate Winder-J5