Math 3090
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Math 3090 An Introduction to Probability Final Exam — Solutions 1. A continuous random variable X has cdf for x ≤ 0, for 0 F(x) = < x < 1, for x ≥ ax2 1. (a) Determine the constants a and b. (b) Find the pdf of X. Be sure to give a formula for fX(x) that is valid for all x. (c) Calculate the expected value of X. (d) Calculate the standard deviation of X. Answer: (a) We must have a = limx→−∞ = 0 and b = limx→+∞ = 1, since F is a cdf. (b) For all x = 0...
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Math 3090 An Introduction to Probability Final Exam — Solutions 1. A continuous random variable X has cdf for x ≤ 0, for 0 F(x) = < x < 1, for x ≥ ax2 1. (a) Determine the constants a and b. (b) Find the pdf of X. Be sure to give a formula for fX(x) that is valid for all x. (c) Calculate the expected value of X. (d) Calculate the standard deviation of X. Answer: (a) We must have a = limx→−∞ = 0 and b = limx→+∞ = 1, since F is a cdf. (b) For all x = 0...