using R :-
A Gumbel random variable X has distribution function
FX (x) = exp (−e^−x).
a) Give a graph of FX and explain using this plot why FX is avalid cumulative probability distri-
bution function.
(b) Find the values of the first and third quartiles and medianX and show their values on the graph.
(c) Make a table of x and FX (x) for x equal to the integersfrom −2 to 5.
(d) Find the probabilities P{−1 < X ≤ 4} and P{4 < X}.
(e) Find the probability density for this distributionfunction.
(f) Provide a second sketch of the distribution function alongwith a sketch of the density function indicating P {−1 < X ≤4}on both pl
