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The percentage of impurities per batch in a chemical product is a random variable X with...

  1. The percentage of impurities per batch in a chemical product is a random variable X with density function

    12x2(1−x), 0≤x≤1 f(x) =

0, elsewhere A batch with more than 40% impurities cannot be sold.

  1. (a) What is the distribution of X?

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Answer #1

given that

(1)

a)

we have to find the distribution of X

Now let Y is type 1 beta distribution with parameters and is given by

let   then

(2)

since (1) and (2) have same pdf

Hence X is type 1 beta distribution with parameters with  

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