Question: Let U be a uniform (0, 1) random variable. (a) Show that V1 = min{U, 1 U} is a uniform (0, 1/2) random variable. (b)

Let U be a uniform (0, 1) random variable. (a) Show that V1 = min{U, 1 U} is a uniform (0, 1/2) random variable. (b) Show that V2 = max{U, 1 U} is a uniform (1/2, 1) random variable. (c) Demonstrate in R the results obtained in (a) and (b): using function runif, generate 1000 values of the random variable U and then plot the histograms of generated values of V1 and V2

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