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# Uniform Distribution Formulas S1. Coding? watch

1. On the Edexcel s1 book I am stuck on Chapter 8 for the s1 book. Especially at page 170/171. I cannot understand the example.

Here is the question:

Digits are selected at random from a table of random numbers

a) Find the mean and standard deviation of a single digit

b) Find the probability that a particular digit lies within one standard deviation of the mean

The book worked it out by using the formulas n+1/2 and (n+1)(n-1)/12

Fair and good. But where the hell did R=X-1 Come out from. I do not understand how to use coding for uniform distribution tables.

Could you please work the problem out explaining the step by step process with a reason for this please?

Thank you.
2. (Original post by Craig David)
On the Edexcel s1 book I am stuck on Chapter 8 for the s1 book. Especially at page 170/171. I cannot understand the example.

Here is the question:

Digits are selected at random from a table of random numbers

a) Find the mean and standard deviation of a single digit

b) Find the probability that a particular digit lies within one standard deviation of the mean

The book worked it out by using the formulas n+1/2 and (n+1)(n-1)/12

Fair and good. But where the hell did R=X-1 Come out from. I do not understand how to use coding for uniform distribution tables.

Could you please work the problem out explaining the step by step process with a reason for this please?

Thank you.
Have a read through from 8.11 again - in particular, the yellow box stating 'Remember to use the formulae the values for X must be 1, 2, 3 ... n'.

So for the question the set R represents the distribution you're interested in - however, you CANNOT use the formulae as the set R has the digit 0 - which messes things up. If you try using the formulae with n=9 you'll find that you get different, incorrect values.

Hence they've shifted all the values up by 1 to get a set X which is of the form 1,2,3 ... n as opposed to 0, 1, 2... n-1

Hence R = X -1, and n becomes 10. It's almost like a map, where 1 from X goes to 0 in R, 2 in X to 1 in R, all the way to 10 in X to 9 in R. So they've mapped it in a way to have all the right values in R but so that they can use the formulae with X.

By properties of expectation and variance you find the expectation and variance of R from the formula, by taking expectation and variance of both sides as they've done in the question.

Let me know if any of that wasn't clear.
3. (Original post by SeanFM)
Have a read through from 8.11 again - in particular, the yellow box stating 'Remember to use the formulae the values for X must be 1, 2, 3 ... n'.

So for the question the set R represents the distribution you're interested in - however, you CANNOT use the formulae as the set R has the digit 0 - which messes things up. If you try using the formulae with n=9 you'll find that you get different, incorrect values.

Hence they've shifted all the values up by 1 to get a set X which is of the form 1,2,3 ... n as opposed to 0, 1, 2... n-1

Hence R = X -1, and n becomes 10 and you can use the formula to find the expectation of X, and so the expectation of R.

By properties of expectation and variance you find the expectation and variance of R from the formula, by taking expectation and variance of both sides as they've done in the question.

Let me know if any of that wasn't clear.
I get it. This means that I have to come up with an equation which will allow me to start the series of number with 1 and go up accordingly..1,2,3...n.
Got it

A question. I have gotten to a question:

A card is selected at random from a pack of cards containing the even numbers 2,4,6,....,20.

The variable X represents the number on the card.

a) Find P(X>15)
b) Find the expectation and variance of X.

Do I have to draw out a probability table to solve the first one?

Then coding for the second one?
4. (Original post by Craig David)
On the Edexcel s1 book I am stuck on Chapter 8 for the s1 book. Especially at page 170/171. I cannot understand the example.

Here is the question:

Digits are selected at random from a table of random numbers

a) Find the mean and standard deviation of a single digit

b) Find the probability that a particular digit lies within one standard deviation of the mean

The book worked it out by using the formulas n+1/2 and (n+1)(n-1)/12

Fair and good. But where the hell did R=X-1 Come out from. I do not understand how to use coding for uniform distribution tables.

Could you please work the problem out explaining the step by step process with a reason for this please?

Thank you.
They want to find the mean and standard deviation for the discrete uniform distribution over the set {0,1,2,3,4,5,6,7,8,9}.

They give formulae for the mean and standard deviation for the discrete uniform distribution over the set {1,2,3,4,5,6,7,8,9,10}.

If you find the mean for the second case you can subtract 1 to find the mean for the first case. The standard deviation is the same in both cases.
5. (Original post by Craig David)
I get it. This means that I have to come up with an equation which will allow me to start the series of number with 1 and go up accordingly..1,2,3...n.
Got it

A question. I have gotten to a question:

A card is selected at random from a pack of cards containing the even numbers 2,4,6,....,20.

The variable X represents the number on the card.

a) Find P(X>15)
b) Find the expectation and variance of X.

Do I have to draw out a probability table to solve the first one?

Then coding for the second one?
For part a) I can't remember what a probability table does, but I'd encourage you to use it and see where it gets you, especially if it's what you've been taught. I would have just thought about what it means when X>15 (how many values satisfy this in the set?) but I suspect that a probability table helps you do the same thing.

b) Yep, coding seems to be the way to go. I hope you can spot the map that turns the set into 1, 2, 3...10.

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Updated: January 27, 2015
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