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3. (20 pts) Acceptance-Rejection Method. 0.465 0.320 0.419 0.218 0.831 0.974 0.275 0.789 0.486 0.267 0.172 0.658 0.142 0.699 0.524 0.429 0.149 0.723 0.787 0.085 0.784 0.322 0.209 0.144 0.531 0.993 0.841 0.817 0.189 0.860 0.634 0.675 0.124 0.2420.047 0.034 0.796 0.740 0.376 0.340 0.840 0.783 0.083 0.761 0.813 0.973 0.970 0.470 0.163 0.734 0.228 0.457 0.084 0.892 0.750 0.643 0.798 0.212 0.372 0.945 0.779 0.5390.003 0.015 0.767 0.198 0.081 0.813 0.108 0.798 0.551 0.763 0.185 0.536 0.243 0.320 0.524 0.924 0.229 0.319 One method for generating random variates is called the acceptance-rejection method. This method requires a random number of uniform(0,1) random variates in order to generate a single random variate of the desired type. Using the uniform(0.1) random numbers given above, you are to generate 10 random variates from the geometric distribution with parameter p = 0.3. A geometric random variable represents the number Bernoulli trials up to and including the first success. The geometric distribution is discrete; it has the following probability mass function. (1-p -p plu) = 0 if x = 1,2,... otherwise Note the parameterization here, which is slightly different from the one given in the book. To generate a single observation from the geometric distribution with parameter p = 0.3, we can consider the uniform(0,1) observations given above as a stream and use the following procedure. (Read the stream from left to right, top to bottom.) (a) Initialize i = 1. (b) Grab a uniform(0,1) observation U, from the stream and set i if U;

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