5. (a) (2 marks) Write a Matlab script that computes a vector of 10000 normal ra

Question

5. (a) (2 marks) Write a Matlab script that computes a vector of 10000 normal random vari- ables, each with mean 5 and standard deviation 2. (b) (4 marks) Write a Matlab script for estimating the probability that a normally dis- tributed random variables with mean 5 and standard deviation 2 is positive. (C) (4 marks) Write a Matlab script for estimating the expected value of g(X) = Xcos(X), where X is a uniform random variable on (1,3). Use vector operations and do not use for loops. (d) (2 marks) Write out the analytical formula for Eg(X)] in part (C). Do not carry out the integration,

Explanation / Answer

a) The vector of 1000 random values drawn from a normal distribution with a mean of 5 and a standard deviation of 2 is given as

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