2. Let X₁,..., X₁ be independent and uniformly distributed on the interval [0, 1]. (a) Write down the pdf for Yi, the ith order statistic. Show that Y; has a Beta distribution. What are its parameters? (b) Find the expected value and the variance of Y₁. (c) Use the previous item to calculate the expected value of Y - Y₁-1, the difference between two successive order statistics. Can you interpret your result?

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Solve the problem below. For your initial post in Brightspace, copy the description of your company given in the box below and then enter your solution to all three parts (parts a, b, and c) of the problem. To copy the description of your company, highlighting and using "copy" from here in Mobius and then using "paste" into Brightspace should work. However, if when you copy and paste x you get a 2 instead, then change your x2 to x^2. Hint: We covered this topic in "2-1 Reading and Participation Activities: Quadratic Equations" in Module Two. You can check your answer to part b to make sure that you are on the right track. For a certain company, the cost for producing x items is 40x +300 and the revenue for selling a items is 80r - 0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression…

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