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#### ethan.lozevski

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« Reply #4530 on: June 03, 2021, 03:53:50 pm »
+1
Hey guys,

I have attached a question that has confused me a little. I used Ali's model and put all my solutions over 19, to sum up to 1 as a pdf requires. Please let me know if I am doing this question correctly. Thanks, guys.

#### fun_jirachi

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« Reply #4531 on: June 03, 2021, 06:44:43 pm »
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Welcome to the forums!

A few questions in return:
- What are the chances you roll a 1 (and subsequently score 4 points) on the new distribution? It is still a fair die.
- Do some values on the original die yield duplicate numbers of points when rolled? What does this do for the probability of scoring a particular y value?

Hope this helps
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#### RuiAce

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« Reply #4532 on: June 03, 2021, 09:47:11 pm »
+3
Hey guys,

I have attached a question that has confused me a little. I used Ali's model and put all my solutions over 19, to sum up to 1 as a pdf requires. Please let me know if I am doing this question correctly. Thanks, guys.
Building onto fun_jirachi's answer here. I would strongly advise considering the second point that he mentioned.

Your table of values is good up until the second row. Then I believe you are confusing yourself with the third row. You want to find the probability distribution for $Y$. Just using the actual values that $Y$ takes on, is not the correct approach here.

Hint: Firstly, what are the values that $Y$ can actually be? (Refer to the second row of your table of values. There are 3 distinct values that $Y$ can take on.) Secondly, for each of those three values of $y$, what is $P(Y=y)$?

#### ethan.lozevski

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« Reply #4533 on: June 04, 2021, 09:17:11 am »
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Thank you for your help. I think I may have read the question incorrectly. Is the following attached image correct?
Thank you.

#### fun_jirachi

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« Reply #4534 on: June 04, 2021, 12:34:29 pm »
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You've addressed my first question - well done!

The second question still stands however.

Hint: Firstly, what are the values that $Y$ can actually be? (Refer to the second row of your table of values. There are 3 distinct values that $Y$ can take on.) Secondly, for each of those three values of $y$, what is $P(Y=y)$?

Should such a distribution have duplicate values for $Y$? If so, how would we amend our probability $P(Y = y)$? Definitely getting closer though, give it another shot
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#### Maroon and Gold Never Fold

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« Reply #4535 on: June 06, 2021, 08:45:07 pm »
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Is anyone able to look over this answer as I am not sure if I have proved it properly or used correct notation. It is the second question of the phtoto (5.ii)

Thanks

#### fun_jirachi

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« Reply #4536 on: June 06, 2021, 08:52:03 pm »
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Seems about right - just be careful with the first line, you haven't subscripted the i, it looks like it's being multiplied onto the numerator as opposed to indexing the score
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#### Maroon and Gold Never Fold

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« Reply #4537 on: June 07, 2021, 06:13:01 pm »
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Seems about right - just be careful with the first line, you haven't subscripted the i, it looks like it's being multiplied onto the numerator as opposed to indexing the score

What do you mean by I haven't subscripted the 'i'. In my picture it is being multiplied on my numerator, is that wrong?

#### fun_jirachi

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« Reply #4538 on: June 07, 2021, 06:24:52 pm »
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Yes - $\sum_{i=1}^{n} \frac{(a+x)i}{n} = \frac{(a+x)(n - 1)}{2}$, which will lead you to an incorrect conclusion. If you notice in the formula that is given for the mean, i is a subscript denoting index (ie. $x_i$ denotes the $i^{\text{th}}$ score). Your first line should be something like $\sum_{i=1}^{n} \frac{(a+x_i)}{n}$.
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#### Maroon and Gold Never Fold

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« Reply #4539 on: June 07, 2021, 09:50:32 pm »
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Yes - $\sum_{i=1}^{n} \frac{(a+x)i}{n} = \frac{(a+x)(n - 1)}{2}$, which will lead you to an incorrect conclusion. If you notice in the formula that is given for the mean, i is a subscript denoting index (ie. $x_i$ denotes the $i^{\text{th}}$ score). Your first line should be something like $\sum_{i=1}^{n} \frac{(a+x_i)}{n}$.

thanks, should I leave the subscript 'i' on 'a' in my second line of working out then.
« Last Edit: June 07, 2021, 09:57:29 pm by Maroon and Gold Never Fold »

#### fun_jirachi

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« Reply #4540 on: June 07, 2021, 10:34:36 pm »
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I wouldn't (since a is not strictly indexed) but it doesn't really matter either way (since a holds a constant value for all i).
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#### neha.singh4

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« Reply #4541 on: July 03, 2021, 09:42:23 pm »
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Hello!

As apart of a maths assessment task I was wondering what were some examples of bivariate data where one pair of variables shows a
positive correlation and the other showing a negative correlation. For example, some that I have are: Arm Length vs Foot Length, Height and Running Speed but am looking for some other ones.

And also what kinds of predictions can you gather from data when interpolating and extrapolating values?

Thank you! Any help would be greatly appreciated!!!

#### fun_jirachi

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« Reply #4542 on: July 03, 2021, 10:20:32 pm »
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Hello!

As apart of a maths assessment task I was wondering what were some examples of bivariate data where one pair of variables shows a
positive correlation and the other showing a negative correlation. For example, some that I have are: Arm Length vs Foot Length, Height and Running Speed but am looking for some other ones.

And also what kinds of predictions can you gather from data when interpolating and extrapolating values?

These are good examples of positive correlation; was there anything in particular you were looking for for your examples? The question is pretty vague

Extrapolating is generally risky, since you can't always guarantee trends and correlation extend to a range values not within your measured range. Interpolation of bivariate data given one variable can allow you to predict with reasonable accuracy the other variable  given a large enough sample size ie. P(Y|X) or P(X|Y).
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#### neha.singh4

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« Reply #4543 on: July 04, 2021, 11:37:29 pm »
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These are good examples of positive correlation; was there anything in particular you were looking for for your examples? The question is pretty vague

Extrapolating is generally risky, since you can't always guarantee trends and correlation extend to a range values not within your measured range. Interpolation of bivariate data given one variable can allow you to predict with reasonable accuracy the other variable  given a large enough sample size ie. P(Y|X) or P(X|Y).

Oh yes that makes sense! Thank you! : ))))

Yes I agree the question is pretty vague too. In terms of what my teacher had explained, she'd like for us to show one set of data that reveals a positive correlation and another set of data that reveals a negative correlation. I was looking for some examples where two sets of variables could fulfill this requirement as well as allow me to analyse data in terms of the Pearson's correlation. Any recommendations?

#### fun_jirachi

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« Reply #4544 on: July 05, 2021, 10:32:11 pm »
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If the question is that vague, you can literally choose anything. Your examples are more than good enough for a possible positive correlation. Most of the data you will be analysing I'd assume would be discrete, but you will always be able to analyse the data in terms of the Pearson correlation coefficient because you can always find the covariance and the variance of the data set(s). For negative correlation, consider some things that may be inversely proportional but not necessarily so, like hours spent on extra-curricular activities vs. grades.
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