Apply the Monte Carlo method to estimate an integral. Le-dx 1 =1/2 (a) (3%) Assume that...

 

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Apply the Monte Carlo method to estimate an integral. Le-dx 1 =1/2 (a) (3%) Assume that you would like to use uniform random variable to approximate I. Rewrite I as an expectation of a function: Specify the function, the random variable, and its distribution. (b) (2%) Follow (a) and write down an algorithm to approximate I. () (3%) Assume that you would like to use the standard normal random variable to approximate I. Rewrite I as an expectation of a function: Specify the function, the random variable, and its distribution. (d) (2%) Follow (c) and write down an algorithm to approximate I. Apply the Monte Carlo method to estimate an integral. Le-dx 1 =1/2 (a) (3%) Assume that you would like to use uniform random variable to approximate I. Rewrite I as an expectation of a function: Specify the function, the random variable, and its distribution. (b) (2%) Follow (a) and write down an algorithm to approximate I. () (3%) Assume that you would like to use the standard normal random variable to approximate I. Rewrite I as an expectation of a function: Specify the function, the random variable, and its distribution. (d) (2%) Follow (c) and write down an algorithm to approximate I.