I have a problem understanding the difference between random variable and random sample. I have read this thread, but still it is unclear.
According to wiki random variable is a function that from a set of outcomes (events) to measurable values $\Omega$ ->$E$ where $E$ could be $\mathbb{R}$. And random sample is a possible outcome.
So, in a lecture script I have these sentences which are confusing me:
let $D=\{x_1,x_2,x_3…x_n\}$ be a set of random variables.
Now I want to create a concrete example for myself to understand what $\{x_1,x_2,…,x_n\}$ could be.
Let's take the sample of two dices where we want to compute the probability of the sum of the figures of dices we have thrown. So we construct a random variable $X$ which just adds the thrown number of the dices:
$$X:\Omega\to\mathbb{N}$$
$$X(\text{dice}_1,\text{dice}_2) = \text{dice}_1 + \text{dice}_2 $$
Where dice are uniformly distributed in $ \{ 1,\cdots,6 \} $.
And as far I know, if I throw two dices, I have concrete values which are my random samples.
Now my concrete question is: what could be in this specific example a set of random variables $D=\{x_1,x_2,x_3…x_n\}$? And what are then the concrete random samples?
UPDATE:
After reading the comments and replies, I want to underline, that I have a specific question and I would appreciate if someone could answer it explicitly:
In the above example please give me a concrete $D = {x_1,x_2,…,x_n}$ as a set of random variables. I want to see how a set of random variables $D = {x_1,x_2,…,x_n}$ (more than 2 random variables) would look like in this example.
Best Answer
This Three Things are totally different let's talk about them one by one
1.Random Variable: Suppose 'x' is a random variable so it can take any value from a positive number system like 1,2,3,4,5....... and so on
There are two types of random variables:
1.discret: which takes discrete value or we can say exact no like 1,2,3,4...
2.continuous: Which Takes Values like from 1 to 10 so we can say it may be 1.1111 or 3.444 or maybe 9.867545 anything
2.Data: Data Means Collection of lots of variables which has some labels like data of maturity in different ages
age-group: [1-10] [10-20]
maturity:-- [0.1] [0.2] So this is Data By which We can Get to the some specific result
3.Random Sample: Part Randomly Taken From Data We can say if we have a large amount of data we can not study on whole data then we take random part of data and them to study on that