# ex1 - 1 Revision Exercises for Probability and Statistics...

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1 Revision Exercises for Probability and Statis- tics 1. Express the following sums in summation notation. (a) X 1 + X 2 + X 3 + X 4 (b) X 3 + X 4 (c) X 1 Y 1 + X 2 Y 2 + X 3 Y 3 + X 4 Y 4 (d) X 1 Y 2 + X 2 Y 3 + X 3 Y 4 + X 4 Y 5 (e) X 2 Y 2 2 + X 3 Y 2 3 2. Write out each of the following sums and compute where possible: (a) 4 i =1 ( a + bX i ) (b) 3 i =1 i 2 (c) 3 x =0 ( x 2 + 2 x + 2) (d) 4 x =2 f ( x + 2) (e) 2 x =0 f ( x,y ) (f) 4 x =2 2 y =1 ( x + 2 y ) 3. Based on past students taking the EBA Introduction to Econometrics course, the probability distribution of X, the number of students absent on Mondays, is as follows: X 0 1 2 3 4 5 6 7 f ( x ) .005 .025 .310 .340 .220 .080 .019 .001 (a) Sketch the probability function of X. (b) Find the probability that on a given Monday either 2, or 3, or 4 students will be absent. (c) Find the probability that on a given Monday more 2, or 3, or 4 students will be absent. (d) Compute the expected value of the random variable X. Interpret this ex-

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## This note was uploaded on 03/14/2010 for the course ECON econmetric taught by Professor Yy during the Spring '10 term at Seoul National.

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ex1 - 1 Revision Exercises for Probability and Statistics...

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