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Let X be a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and...

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Basic Math

Let X be a random variable with CDF F(x) =e-e(µ-x)/β, where β > 0 and -∞ < µ, x < ∞.

1. What is the median of X?

2. Obtain the PDF of X. Use R to plot, in the range-10

3. Draw a random sample of size 1000 from f(x) for µ = 2, β = 5and draw a histogram of the values in the random sample drawn.Compare this histogram with the answer in 2 above.

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