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Unformatted text preview: ECEN 303: Assignment 7 Problems: 1. Let X have the PDF f X ( x ) = Î» 2 e- Î» | x | , where Î» is a positive scalar. Verify that f X satisfies the normalization condition, and evaluate the mean and variance of X . 2. Consider a traingle and a point chosen within the triangle according to the uniform probability law. Let X be the distance from the point to the base of the triangle. Given the height of the triangle, find the CDF and the PDF of X . 3. Consider two continuous random variables Y and Z , and a random variable X that is equal to Y with probability p and Z with probability 1- p . (a) Show that the PDF of X is given by f X ( x ) = pf Y ( x ) + (1- p ) f Z ( x ) . (b) Calculate the CDF of the two-sided exponential random variable that has PDF given by f X ( x ) = braceleftBigg pÎ»e Î»x , if x < , (1- p ) Î»e- Î»x , if x â‰¥ , where Î» > 0 an 0 < p < 1. 4. Let X be a random variable with probability density function f ( x ) = braceleftBigg c ( 1- x 2 )- 1 < x < 1 otherwise ....
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- Fall '07
- Probability distribution, Probability theory, probability density function, Cumulative distribution function, CDF