Use R to complete the following questions. You should include your R code, output and plots...

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Basic Math

Use R to complete the following questions. You should includeyour R code, output and plots in your answer.
1. Two methods of generating a standard normal random variableare:
a. Take the sum of 5 uniform (0,1) random numbers and scale tohave mean 0 and standard deviation 1. (Use the properties of theuniform distribution to determine the required transformation).
b. Generate a standard uniform and then apply inverse cdffunction to obtain a normal random variate (Hint: use qnorm).
For each method generate 10,000 random numbers and check thedistribution using
a. Normal probability plot
b. Mean and standard deviation
c. The proportion of the data lying within the theoretical 2.5and 97.5 percentiles and the 0.5 and 99.5 percentiles. (Hint: Theifelse function will be useful)

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r code random number generate and output uniform random number sample size n5 urunifn501 u 1 001102249 039552950 078375498 002191521 075244598 sumu 1 1964668 ameanua 1 03929336 bvarub 1 0141377 sdsqrtbsd 1 03760013 inverse method use genrate random number n5 urunif5 u 1 013909559 009987109 011123441 001423793 086949264 aqnormua 1 1084392 See Answer

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