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11ProbHw7

# 11ProbHw7 - IEOR 3658 Probability Prof Mariana...

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IEOR 3658 Assignment #7 Probability October 26, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #7 – due November 2nd, 2011 1. Consider a random variable X that takes values in the interval (0 ,a ) whose density function has a triangular shape and is given by f X ( x ) = ( bx + c, for 0 x a, 0 , otherwise. with b < 0. (a) Find the constants b and c and plot the PDF. (b) Compute and plot the CDF of X . 2. Let Y be a random variable having PDF f Y ( y ) = ( K (1 - y ) 2 y, if 0 y 1 0 , otherwise. for some constant K > 0. (a) Find the value of K . (b) Compute the mean and the variance of Y . 3. (From text) Consider a triangle 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 . 4. (From text) Calamity Jane goes to the bank to make a withdrawal, and is equally likely to ﬁnd 0 or 1 customers ahead of her. The service time of the customer ahead, if present, is

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11ProbHw7 - IEOR 3658 Probability Prof Mariana...

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