Question: Question 3 (10 marks): A continuous random variable X is said to have the Normal distribution with mean ,u and variance 02. a) (4 marks)

Question 3 (10 marks): A continuous random variable X is said to have the Normal distribution with mean ,u and variance 02. a) (4 marks) Give an expression for the median and interquartile range (IQR) of X. Hint: IQR is equal to the difference between the 75th and 25th percentiles. b) (3 marks) Prove that E [IX ul] = (Kl; c) (3 marks) Assume ,u = 0 and 02 = 1 such that X follows a standard Normal distribution. Let S = X 2, find the probability density function of S, f5(s)

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