Question: Let Y be a continuous random variable with probability density function: f(y) = ky k(2 y) 0 y 1 1 y 2 0 otherwise

Let Y be a continuous random variable with probability density function: f(y) = ky k(2 y) 0 y 1 1 y 2 0 otherwise a. Find the value for k so that f(y) is a probability density function (5 points) b. Find the cumulative distribution function of Y. (5 points) c. Find the median value of Y. (5 points) d. What is the probability that Y is greater than 1.5? (5 points) e. Given that Y is greater than 1.5, find the probability that Y is less than 1.75. (5 points)

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