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i. If a variable has mean 3 and standard deviation 5, then find mean and variance of Y = 2 X + 5 ii. A moderately skewed distribution has mean 30 and mode 36. Find median. iii. Mean of a series is 10 and its coefficient of variation is 40%. What will the value of variance of the series? iv. Two series have XA = 15.0, X = 20.0, $1 = 25, $, = 16, Which series is more consistent? v. What do you say about skewness of the distribution if Median is 49.21 while two quartiles are 37.15 and 61.27 respectively. vi. Given P(A) = 0.60, P(B) = 0.40, P(AnB) = 0.24, find P(A/B), P(AUB) b) Differentiate the following terms with real life examples. (3) i. Scientific and random experiment ii. Dependent and independent events iii. Mutually and non-mutually exclusive events Q. 2 a) What can you say about Skewness and Kurtosis of a distribution, if First 4 moments about A = 20 are given as -0.3, 44.5, -52.5 and 5462.5 respectively. (8) b) Consider the following data: (7) X 3 5 6 9 10 12 20 22 28 Y 10 12 15 18 20 22 27 30 32 34 Show that E(Y-Y) = 0 ii. Find coefficient of correlation between X and Y and interpret it. Q. 3a) Two fair dice are rolled. Find the probability of the events defined by: (6) i. A = {(a, b) : a + bs 10} ii. B = {(a, b) : la- bl