homework01

homework01 - X (1) , X (2) , , X ( n ) of a sequence of...

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Probability for Engineering Applications Assignment #1, due at the beginning of class on Thursday, January 26 th , 2006 1. (3 pts) Write a program using the C programming language to generate 1000 random integers in the range 0 to 8191. Use the following recursive formula to generate the numbers: X ( i ) = αX ( i - 1)mod M i = 1 , 2 , · · · , 1000 where M = 8191. Use the following two values for α : 128 and 126. You can choose any positive integer as X (0). What is the qualitative diFerence in their outputs? (Note that you have to use C or C++ and no other language or platform/package is allowed). You have to submit the program also (a printout of the program is su±cient). 2. (4 pts) (Textbook exercise 1.7) the sample mean of a series of numerical outcomes
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Unformatted text preview: X (1) , X (2) , , X ( n ) of a sequence of random experiments is dened by h X i n = 1 n n X j =1 X ( j ) Show that the sample mean follows the following recursion formula: h X i n = h X i n-1 + X ( n )- h X i n-1 n , h X i = 0 3. (3 pts) Use the last expression in Question 2 to calculate the sample mean of the 1000 pseudo random numbers generated in Question for both = 128 and = 126. Plot h X i versus n and determine if the sample mean is converging to any particular value as the number of samples increases or if there is any other trend in the curves. 1...
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