Distribution of balls in a box (with a twist)

[Apteronotus]

Suppose I have an box (set) containing two different colored balls, red and blue, say.

Now, suppose the balls differ in size, where the size of the red balls has one particular distribution and those of the blue another.

How can we describe the distribution of the balls in the box?

 

[mathman]

Your description is confusing. What has size got to do with the distribution?

 

[FactChecker]

Suppose I have an box (set) containing two different colored balls, red and blue, say.

Now, suppose the balls differ in size, where the size of the red balls has one particular distribution and those of the blue another.

How can we describe the distribution of the balls in the box?

It's a weighted average of the PDF_red and PDF_blue, with weights proportional to the fraction of each color:

PFD_total = (num_red/total_num) * PDF_red + (num_blue/total_num) * PDF_blue

 

[Apteronotus]

Your description is confusing. What has size got to do with the distribution?

I'm interested in the distribution of the sizes.

 

[Apteronotus]

It's a weighted average of the PDF_red and PDF_blue, with weights proportional to the fraction of each color:

PFD_total = (num_red/total_num) * PDF_red + (num_blue/total_num) * PDF_blue

So would it be a "mixed distribution"?

 

[FactChecker]

So would it be a "mixed distribution"?

It is a single distribution where a ball can be picked at random by a blind person and it would give the probability distribution of the size, without knowing the color. It combines the two distributions into one.

 

[FactChecker]

So would it be a "mixed distribution"?

Yes. That is called a "mixture distribution".