Once you have a Probability Mass Function you can determine conditional probability.
Sample Space - The set of all possible outcomes for a probabilistic trial. For the case of rolling a single die, the sample space would be \left \{ 1,2,3,4,5,6 \right \}{1,2,3,4,5,6}
Normalized
sum of probabilities of all events = 1.
Any mathematically correct distribution must be normalized, but un-normalized distributions can also be useful if we just want to compare relative probabilities.
Conditional Probability
The conditional probability p(A|B)p(A∣B) gives the probability of event A given that event B has already occurred.
Probability Distribution
A mapping of events to probabilities. For a discrete distribution we can use a table like the following for a fair die:
Event
Probability
1
1/6
2
1/6
3
1/6
4
1/6
5
1/6
6
1/6
Random Variable - A random variable is a variable whose possible values are outcomes of some random phenomenon.
5. Expected Value
Tells us the result of the random variable at any given time.
6. Variance
How spread out are these values around the mean x_bar.
It’s an expression of how well we know the mean. It’s a confidence. It tells us how much the samples vary.
Expected Value - The expected value gives the long-run average value of a repeated probabilistic experiment. Mathematically, the expected value of a random variable X is defined as:
Variance - The variance of a random variable measures how spread out a set of numbers are from their mean(expected value).
Standard Deviation - The standard deviation is a common measure of spread. It's just the square root of the variance.
4. Review of Discrete Probability
5. Expected Value
6. Variance
8. Probability Density Function