quiz4 and ans - AMSC/CMSC 660 Quiz 4 Fall 2006 1(10 Write...

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AMSC/CMSC 660 Quiz 4 , Fall 2006 1. (10) Write Matlab code using rand to generate a random number from the following distribution: The probability that the number is 0 is 0.6. The probability that the number is 1 is 0.4. (In other words, if p ( x ) is the probability density function, then p (0) = 0 . 6 and p (1) = 0 . 4 .) Answer: % In this code, % z is a sample from a uniform distribution on [0,1]. % y is a sample from the desired distribution. z = rand(1); if (z < .6) y = 0; else y = 1; end 1
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2. (10) Write Matlab code to compute the volume of the unit sphere x 2 1 + x 2 2 + x 2 3 1 using Monte Carlo integration. (You may use any of our three methods, although I suggest not using importance sampling because it is harder to write down.) Answer: Here are implementations of “Method 1” (5 lines of Matlab code) and “Method 2” (8 lines of code). % "Method 1": We compute the volume of the unit sphere % as 8 times the volume of the piece of it in the 1st orthant % (x_1 >= 0, x_2 >= 0, x_3 >= 0). Call this piece Omega.
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