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  3. using r :- a gumbel random variable x has distribu

using R :- A Gumbel random variable X has distribution function FX (x) = exp (−e^−x). a) Give...

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Statistics

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

Answer & Explanation Solved by verified expert
3.7 Ratings (497 Votes)
The distribution function of the Gumbel random variable isa The graph of is plotted belowR code belowcurveexpexpx xlimc57ylim    See Answer
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