An ice cream seller takes 20 gallons of ice cream in her truck each day. Let X stand for the number of gallons that she sells. The probability is 0.1 that X = 20. If she does not sell all 20 gallons, the distribution of X follows a continuous distribution with a p.d.f. of the form

f(x) = {ex 0< x < 20
0, otherwise

Find the constant c.

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joaobezerra joaobezerra · Answer 1 · 2022-08-12T20:00:31+02:00

Considering the given probability distribution, the constant c is given by: c = 0.0045.

We have to consider the distribution given by:

We have that P(X < 20) = 0.9, and this is represented by the following definite integral:

[tex]P(X < 20) = \int_{0}^{20} cx dx[/tex]

Hence, applying the rule for the integral of the power of x, we have that:

[tex]P(X < 20) = 0.5cx²|_{x = 0}^{x = 20}[/tex]

Then, applying the Fundamental Theorem of Calculus:

200c = 0.9.

c = 0.9/200

c = 0.0045.

Hence the constant c is given by: c = 0.0045.

More can be learned about probability distributions at https://brainly.com/question/22583815

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