2. (8 points) A group of students has 3 hours to complete a final exam. The...

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2. (8 points) A group of students has 3 hours to complete a final exam. The time a given student will spend working on the exam, X, is a continuous random variable with the cumulative distribution function F(x) = cx2 for 0 x 3. 2.1. What is the value of the constant, c? *2.2. For a continuous random variable, X, the cdf may be found by integrating the pdf of X. Therefore, if you know the cdf of X, you can find the pdf by differentiating the cdf with respect to x. Find the pdf of X for 0 < x < 3, and use it to compute, by integration, the expected amount of time it will take a student to complete the exam. 3. (8 points) Let the median, or 50th percentile, of any random variable be the value satisfies F(xp50) = 0.5. In the biathlon problem we did in class, you found that the cdf of X, the distance the bullet lands from the center of the target area, is F(x) = - for 0 x 4. Xp50 that 3.1. What is the median distance the bullet will land from the center? (Hint: use the quadratic formula.) 3.2. Is this distribution skewed left, skewed right, or symmetric? 2. (8 points) A group of students has 3 hours to complete a final exam. The time a given student will spend working on the exam, X, is a continuous random variable with the cumulative distribution function F(x) = cx2 for 0 x 3. 2.1. What is the value of the constant, c? *2.2. For a continuous random variable, X, the cdf may be found by integrating the pdf of X. Therefore, if you know the cdf of X, you can find the pdf by differentiating the cdf with respect to x. Find the pdf of X for 0 < x < 3, and use it to compute, by integration, the expected amount of time it will take a student to complete the exam. 3. (8 points) Let the median, or 50th percentile, of any random variable be the value satisfies F(xp50) = 0.5. In the biathlon problem we did in class, you found that the cdf of X, the distance the bullet lands from the center of the target area, is F(x) = - for 0 x 4. Xp50 that 3.1. What is the median distance the bullet will land from the center? (Hint: use the quadratic formula.) 3.2. Is this distribution skewed left, skewed right, or symmetric?