An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with the following pdf. f(r)={34(1−(14−r)2)13≤r≤150 otherwise
What is the expected area of the resulting circular region?

the expected area of the resulting circular region is 616.38 m²

Step-by-step explanation:

Given that:

otherwise

The expected area of the resulting circular region  is:

=

=

To calculate

Recall:

The expected area of the resulting circular region  is:

=

=

where;

Then

The expected area of the resulting circular region  is:

=

= 616.38 m²

"if it is my birthday, then it is snowing"

yes. we do proportions in probabilities.