Following on from finding the expectation of a discrete random variable, we will now look at finding the variance of a discrete random variable – another common exam question.
The expectation of a discrete random variable is its mean. Every discrete random variable has an expectation, and the expectation of a variable isn’t likely to be the same between two different variables.
When you expand a bracket many times, a pattern starts to emerge. You can use this pattern to quickly determine the final sum of the expansion, or to find a single coefficient of an expanded variable.
The pattern that emerges can be thought of as a series of numbers. This is because each expansion follows the same pattern, so we can predict the next expansion. This is why binomial expansion is also known as “binomial series”
For the Edexecel C2 mathematics exam, there are two trigonometric identities you need to learn – you may also have to rearrange the two identities.
Just like the arithmetic series we see in C1, C2’s geometric series describe a pattern that emerges from a string of numbers.
The difference between the two is that arithmetic series add numbers together, while geometric series multiply numbers together. Because of this, our common difference from arithmetic series is replaced with a common ratio .
All formulas in this post are given to you in the exam.
Discrete random variables (DRVs) are variables whose probability distribution only contains discrete values – this means the variable can only take certain values: it represents discrete data.
Young Modulus is a measure of how much a material will extend under a given pressure (stress). Young modulus is constant for a given material, as long as the material hasn’t exceeded its elastic limit.
In Physics, stress is a measure of the pressure a material is under, which can be called the force per unit of area.
In Physics, strain is a measurement of how much a material has stretched.
Two’s complement is the system used by computers to represent negative numbers in their binary form. The system is actually very straightforward, so it shouldn’t take long to get the hang of it!
In Two’s complement, all negative numbers are represented by a leading “1” – that is: their first digit (starting from the left) is a 1. You then work backwards, and all digits that are represented by a “1” you subtract from the leading value.