120PS2 - 1(b Calculate the variance of the uniform...

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Problem Set 2 - Econometrics 120A Due Monday Oct 17 1. Suppose you roll a die 5 times. Let X be the number of sixes that were rolled. In this exercise we will examine the distribution of X . (a) Write down the probability mass function (pmf) for X for all the values that X can take. (You may find the function BINOMDIST in Excel helpful). (b) Write down the cumulative distribution function (cdf) for X . (c) Calculate the mean of X (d) Calculate the standard deviation of X . 2. In class we talked about how the pmf tells you everything you need to know about a discrete random variable. The cdf also contains the same information as the pmf. To illustrate the point, recover the pmf from the cdf in the example below: p ( x ) = P ( X = x ) (pmf) F ( x ) = P ( X x ) (cdf) X = 0 0 X = 1 0.1 X = 2 0.5 X = 3 1 X = 4 1 3. Recall that the probability distribution function (pdf) for the uniform distribution on the interval [0 , 1] is given by p ( x ) = 1. (a) Calculate the mean of uniform distribution on [0
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Unformatted text preview: , 1]. (b) Calculate the variance of the uniform distribution on [0 , 1]. (c) The function RAND in excel draws one observation from the uniform distribution on [0 , 1]. Create 500 observations from the uniform distribution in this way. (Note: You don’t have to type RAND 500 times. Just do it once, then choose the cell with the entry and move the mouse to the bottom right corner. The cursor should change to a thinner cross. Click and drag down 500 cells. This should copy down the RAND function to all the cells below). Find the average for the first 10 observations, for the first 100 and for the first 500. (d) Find the variance for the first 10 observations, the first 100 and the first 500. (e) How do your answers in (c) and (d) compare to your answers in (a) and (b)? Why? 4. 4-20 (page 133) and 4-22 (page 134) 1...
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