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Let X be a random variable with cumulative distribution funtion0.pdf

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Let X be a random variable with cumulative distribution funtion 0, if x< 0, 1, if 1 < x. b) What is the probability that X < 1/4? Solution fx = derivative of F(x) = 0 if x<0 (pi/2)*sin(pi*x) if 0<=x<=1 0 if x>1 P(x> 1/4) = integration of fxdx from - to 1/4 = integration of (pi/2)*sin(pi*x)*dx from 0 to 1/4 = -cos(pi*x)/2 limits from 0 to 1/4 = (1 - cos(pi/4))/2 = 0.1464.

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Let X be a random variable with cumulative distribution funtion 0, if x< 0, 1, if 1 < x. b) What is the probability that X < 1/4? Solution fx = derivative of F(x) = 0 if x<0 (pi/2)*sin(pi*x) if 0<=x<=1 0 if x>1 P(x> 1/4) = integration of fxdx from - to 1/4 = integration of (pi/2)*sin(pi*x)*dx from 0 to 1/4 = -cos(pi*x)/2 limits from 0 to 1/4 = (1 - cos(pi/4))/2 = 0.1464

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Let X be a random variable with cumulative distribution funtion0.pdf

  • 1. Let X be a random variable with cumulative distribution funtion 0, if x< 0, 1, if 1 < x. b) What is the probability that X < 1/4? Solution fx = derivative of F(x) = 0 if x<0 (pi/2)*sin(pi*x) if 0<=x<=1 0 if x>1 P(x> 1/4) = integration of fxdx from - to 1/4 = integration of (pi/2)*sin(pi*x)*dx from 0 to 1/4 = -cos(pi*x)/2 limits from 0 to 1/4 = (1 - cos(pi/4))/2 = 0.1464