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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
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 + αx 2 , −1 ≤ x ≤ 1, −1 ≤ α ≤ 1
67. The Weibull cumulative distribution function is F(x) = 1 − e−(x/α)β , x ≥ 0, α> 0, β> 0 a. Find the density function. 70 Chapter 2 Random Variables b. Show that if W follows a Weibull distribution, then X = (W/α)β 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.
