Chapter 6 Statistical Distributions - Year 1 Flashcards
What does this mean?
How do you convert a piecewise function into a table?
You write in the top columns all the possible values of x
In the bottom column you put what you get when you have that value of x (you may have to substitute the value into an equation)
What is a key piece of information to remember in this topic?
The chance of something happening is 1
What do you need to remember to do in a piecewise function?
At the bottom have 0, otherwise
What is a general rule of thumb that makes things easier with piecewise functions?
Write them out in a table
What do you do here?
Solve for x to make it into the right form
Draw the piecewise function for rolling a dice?
Give an example of discrete uniform distribution?
A throw of a dice
What is discrete uniform distribution?
When the probability of each outcome is the same
If you are asked about the probability distribution of cloud cover what do you need to remember?
0/8 is one of the options so there is 9 different things that could happen
When can you model something using binomial distribution?
There are a fixed number of trials
There are 2 possible outcomes: “success” and “failure”
There is a fixed probability of success
The trials are independent of each other
What is the first thing you write out when doing a binomial distribution question?
Where n is the number of trials
Where p is the FIXED probability
What is the full method of using the binomial distribution?
The same as binomial expansion
After you write out the first step of X~B(n,p)
You do:
What does the binomial CD do?
Give you the value of it happening up to x
What does the binomial PD do?
Give you the value of it happing x times
How do you use the binomial distribution to work out cumulative frequencies FROM THE BOOK?
You go to page 29 of the formula booklet. You go to the correct p column then down to the correct n then the correct x and that is your value
How do you use the binomial distribution to work out cumulative frequencies ON THE CALCULATOR?
Menu
7 - Distribution
Down arrow
1 - Binomial CD
2 - Variable
Input Data
=
What is very specific in cumulative probabilities in the binomial distribution?
You are working out
NOTHING ELSE
When transforming a probability thing how do you switch the direction of the inequality?
1-P(X…
What is the key to rearranging the probability things?
To think about what numbers you want
How do you rearrange the probability thing when it is a greater/less than and NOT equal to?
You decrease it by 1
How do you use binomial CD to work out P(X=100)
How do you do a binomial CD question when you are told to find how many of x is needed to make the chance of winning z?
Write out the probability thing but in terms of x and with an inequality with the wanted chance of success is
Then rearrange so that the probability thing is in the write form
Then rearrange so that it is in the form of a number on 1 side and a probability thing on the other side
Then find the first value in the formula booklet that is either greater than or less than the number (quick check is to substitute the value into the inequality does it make sense?(labeled appendix 1))
Then you either get n= or more likely n-1= and solve for n
If there is an unknown in the probability thingy what are you going to need?
The formula booklet
How do you solve a probability thingy with an unknown in it?
You rearrange to get the probability thingy in the correct form (this could including changing n to n-1)
Then go to the formula booklet and find the first value that is greater than or less than other side of the inequality
What is an easy way to check that your answer to the unknown probability question is the right one?
Substitute your value into the equation.
The inequality should still make sense
