My professor and I disagree on a test's answer. would love to get a second opinion.

[arielk]

The question is as follows:
"
In a certain country:
10% of the families have no children
20% of the families have 1 child
30% of the families have 2 children
40% of the families have 3 children

one child is randomly chosen from all the children in the country.

X is a random variable whose value is the number of brothers/sisters said sampled child has.
"

What is the probability function of X?


notes:
1 - the underlines are from the original test question
2 - let me know if you want to see my answer against that of my professor. I thought it might be better to see how you answer without any former bias - but i might be mistaken about that(too? :< )

Thanks!

 

[BGM]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

A little bit tricky if you answer the question in full tempo. With a second thought you should obtain these?

\( \Pr\{X = 0\} = 0.1, \Pr\{X = 1\} = 0.3, \Pr\{X = 2\} = 0.6 \)

 

[arielk]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

That's exactly what I answered!

The "Official answer" though is:

X=0 = 2/9
X=1 = 3/9
X=2 = 4/9

And god help me - I can't understand why.

 

[Karabiner]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

If you consider questions about a radomly selected child,
then not 100 families but only 90 families (those with
children) are of interest?

With kind regards

K.

 

[arielk]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

of course, but then the question is how many children are there in those 90 families?
according to what BGM and I did - it's 200 kids in total and then the probabilities are as BGM wrote.

 

[BGM]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

There is nothing to argue. Obviously your professor want to set a simple question about the truncated distribution, but used a wrong/ambiguous wording which mislead a careful student like you. Your professor simply mean he randomly select a family in his mind.

 

[Rhodo]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

If you look at a simple case of 10 families, then 1 of these families has 0 kids, 2 of them have 1, 3 of them have 2 and 4 of them have 3. Given that you've sampled a child, you know that the one family with 0 kids is now irrelevant because it's impossible that you've sampled from their family. You either sampled from one of the two families with 1 child, the three families with two, or the four families with 3. The probability of sampling from a family is the amount of instances of that type of family divided by 9 since, as was mentioned, the case of the family with 0 children is not possible given a child was selected.

I hope that makes sense.

 

[Dason]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

If you look at a simple case of 10 families, then 1 of these families has 0 kids, 2 of them have 1, 3 of them have 2 and 4 of them have 3. Given that you've sampled a child, you know that the one family with 0 kids is now irrelevant because it's impossible that you've sampled from their family. You either sampled from one of the two families with 1 child, the three families with two, or the four families with 3. The probability of sampling from a family is the amount of instances of that type of family divided by 9 since, as was mentioned, the case of the family with 0 children is not possible given a child was selected.

I hope that makes sense.

It sounds like you're talking about sampling the families though. As BGM points out - in a family with 2 kids.... there are 2 kids to sample from according to the wording of the question. So in your example there are:
2 kids from families that only have 1 kid,
6 kids from families that have 2 kids,
12 kids from families that have 3 kids

which gives 20 children total to sample from.

 

[Rhodo]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

ah, I see what you mean.

 

[dj_johnphillips]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

If you'll forgive the poor layout (can't work out how to do a nice table on the forum just now). I'd probabley structure my answer as follows. (Commas denoting where the table colums should be)...

Proportion of Families,No of children,Total Children,Proportion of Children
1,0,0,0
2,1,2,1/10
3,2,6,3/10
4,3,12,6/10
Total,,20,

So
P(x=1) = 0.1, P(x=2) = 0.3, P(x=4) = 0.6, Otherwise P(x) = 0

 

[arielk]

Re: My professor and I disagree on a test's answer. would love to get a second opinio

Hooray, my appeal was granted and my answer was deemed correct.
many thanks go to you as I have mentioned this forum as a place where I "double checked" my answer