I could use some pointers on how to get started with an R Code Assignment.
65. How could random variables with the following density function be generated from a uniform random number generator? f (x) = 1 + ?x 2 , ?1 ? x ? 1, ?1 ? ? ? 1
67. The Weibull cumulative distribution function is F(x) = 1 ? e?(x/?)? , x ? 0, ?> 0, ?> 0 a. Find the density function. 70 Chapter 2 Random Variables b. Show that if W follows a Weibull distribution, then X = (W/?)? follows an exponential distribution. c. How could Weibull random variables be generated from a uniform random number generator?
For problems 65 and 67 please do the following: (a) use R to generate 10,000 random values (using an alpha of 0.25 for problem 65, and alpha of 1, beta of 4 for problem 67) and plot the estimated pdf and cdf. (b) use the random values to find the probability that X is between 0.2 and 0.8 and calculate and compare this to the truth. (c) use the random values to estimate Q1, M, and Q3 and compare these to the truth.