You are Here: Home >< Maths

# further maths statistics help? watch

1. really stuck on these questions, would appreciate any help please

1.) a random number X is chosen from the fractions 1/n,2/n,3/n.....1
prove that the expectation of X >1/2, but the variance of x < 1/12

2.) X~U(n). prove that 6 Var(X) is always divisible by E(X)

Any help appreciated, thanks
2. What type of probability distribution is it? How do you calculate expectation of a random variable?
3. And think about how you sum up the first n natural numbers.
4. It'd be better if you post the actual questions tbh.
But regardless, you can rewrite the fractions as 1/n, 2/n, 3/n, ...., n/n (1).

So the expectation would be the mean: the sum of all the fractions divide by the number of them:

Notice the link here is that 1 + 2 + ... + n is the sum of all the natural numbers.

You can also use the formula where is 1.
We know that the probability of choosing each fraction or value of X from the distribution is equal, (1/n).
So, using the formula:

Once you find that out, you should notice the clue: as n is a the number of terms in the series, it must be a positive integer.

I hope you can take it from there.

For the second part, I'm not sure waht you mean. X~U[n]. I'm assuming it's X~U[0,n].
Use the formula for the variance and mean of a continuous uniform distribution and you'll understand it from there.
5. Latex is a clear nightmare, anyway good luck lol.
6. (Original post by Chittesh14)
Latex is a clear nightmare, anyway good luck lol.
LaTex is great.

You're welcome.

Also check this:

(Original post by Chittesh14)
Notice the link here is that 1 + 2 + ... + n is the sum of all the natural numbers.
7. (Original post by RDKGames)
LaTex is great.

You're welcome.

Also check this:
Thanks buddy .

Btw, what is there to check? :O
I missed 0, but no difference to sum lol.
8. (Original post by Chittesh14)
Thanks buddy .

Btw, what is there to check? :O
I missed 0, but no difference to sum lol.
It's not the sum of all natural numbers.
9. (Original post by RDKGames)
It's not the sum of all natural numbers.
Why not?
10. (Original post by Chittesh14)
Why not?
Because you stop summing them at some point lol...
11. (Original post by RDKGames)
Because you stop summing them at some point lol...
Oh right lol fair enough.
12. rickyrossman TeamXO Chittesh14 RDKGames
13. (Original post by MattDwyer)
rickyrossman TeamXO Chittesh14 RDKGames
No worries .

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 13, 2018
Today on TSR

### A-Level OCR Biology Unofficial Markscheme

Find out how you've done here

### 3,638

students online now

Exam discussions

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams