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Question 1 [11 marks] A continuous random variable X is said to follow a "half normal" distribution if it has the density function fx(x) = ce /2 for r > 0 where c is a constant. (a) Demonstrate that the constant c must equal for fx (x) to be a valid density function. (b) Find the mean of this distribution. (c) A regularized lower incomplete gamma function at point t with parameter o is defined as I(t, a) = (a ) yo-le-ydy where I'(a) is the standard gamma function. Express the cdf Fx(x) in terms of the regularized lower incomplete gamma function. Apply reasonableness checks to Fx(x). Using R, plot the cdf Fx(x)