11:16 * NE 49 .ill .ill 45% New Microsoft Word Document (2) . . . Subject: Statistics Course Code: STAT-1201 Course Title: Introduction to Probability Distributions Time Allowed: 3 Hours Q#1: a) Differentiate between discrete and continuous random variable, give real life examples to support your answer. b) The joint probability distribution of two random variables X and Y is given as: X f(x y) 2 0.20 0.05 0.05 2 0.0 0.35 0.05 0.05 0.10 0.10 (1) Find the marginal distributions of X and Y. (ii) Find E(X) and E(Y). (iii) Find the conditional distribution of X, given that Y=2 and P(X=3| Y=2). iv) Determine whether the two variables are dependent or independent. Find correlation between X and Y. Q#2: a) Distinguish between binomial and negative binomial distributions. Use practical examples to explain the concept. b) A survey reports that, about three-fourth of the 1.5 million persons in a city who take diazepam to treat anxiety, alcohol withdrawal, and seizure etc. are females. Find the probability that on a given day the sixth prescription written by a doctor for diazepam is: (i) the first prescribing diazepam for a female (ii) the fourth prescribing diazepam for a female c) On a busy airport an aero-plane lands after an average of 15 minutes. Based on Poisson distribution what is the probability that in a 15 minutes interval, 3 or more aeroplanes will land? O