Find the marginal distribution of age group

Question

Age group 15 to 19 years, 2124 Females and 1876 Males

Answer 1

A marginal distribution is a way of focusing on one of several variables and ignoring the rest. Here is a simple example. Say you flipped two coins and someone wants to figure out whether coin 2 is biased.

 

Coin flip results:

Coin 2\Coin 1 Heads Tails

Heads            20      10

Tails               60      35

 

Someone who wants to find out something about coin 2 from this data looks at how many times coin 2 came up heads or tails. They would add the values for coin 1 coming up heads and tails, since that does not affect the category that the trial falls in : coin 2 heads or coin 2 tails is unaffected by the status of coin 1. This gives 30/95 as the marginal probability that coin 2 comes up heads, so the marginal distribution is: heads 30/95, tails 65/95. Note that this is distinct from the conditional distribution; for that, you narrow down the search by specifying a value for coin 1 and seeing the distribution that coin 2 follows for just that value of coin 1.

 

Hopefully, this helps with your problem - it looks like some lines got cut off, so an explanation of the topic is all I can give you.

Answer 2

Hello, thank you for taking the time to post your question!

Did it give you any additional details beyond that? Typically in order to form a marginal distribution there would be data for multiple age groups, such as 20 to 24 years, 25 to 29 years, and so on to get the total counts for each group. The total for this one of the group ages 15 to 19 years is

2124 + 1876 = 4000, but typically you want to know how that compares to other age groups in order to make a comparison for the marginal distribution

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)