Discrete Probability Distributions Flashcards
What is a random variable?
A variable whose value depends on the outcome of an event
What is a sample space?
The range of values that a random variable can become
What is a discrete variable?
A variable which can only take up certain numerical values
What is a probability distribution?
A table or probability mass function which describes the probability of every outcome in the sample space
What does P(X = x) mean?
The probability that a random variable X (such as the outcome of flipping a coin) is equal to x (which its one of the values of the random variable, such as tails)
What can be said about the total of a probability mass function?
Total probability must always equal 1 just as with any other probability
What should be stated next to ‘otherwise’ in a probability mass function?
0
In reference to any other variables being impossible
How should a table showing probability distribution be set out?
x values listed along the side with P(X = x) stated for each
How do you go about creating a probability mass function?
- List all outcomes in the sample space
- Find probability of each occurring
- Write P(X = x) = ( )
-Within the bracket, state the different probabilities on the left with the corresponding values for x on the right - Any variables with matching probabilities, write in the same column
What is a discrete uniform distribution?
A probability distribution in which the probabilities of each outcome are the same (six-sided dice or flipping a coin)
How is distribution shown for a continuous random variable?
Using a probability density function (PDF)
Taking the area under the graph of this function represents probability
PDF’s are usually noted as f(x)
What are the axis labels for a probability density function graph?
Y-axis : f(x) which is the probability density function
X-axis : x which represents all values in the sample space
Why can you not take a point on a probability density function graph and find probability from there?
PDF graphs show the probability over intervals
If you take one point on the graph, P(X = x) = 0 as the data is continuous and so has infinite precision
How is P(a<X<b) found on a probability density function graph?
The integral of f(x) with limits a & b
