Describe the concept of a sample space, and exemplify it with the outcome of a coin toss
A sample space is a nonempty set of all possible outcomes from a random experiment and commonly denoted with the greek letter omega. For instance the omega of a coin toss is as below:
Define a partion of a sample space
What is a sigma algebra
A collection of subsets within the probability space that satisfy 3 conditions:
What property is true for a sigma algebra with respect to intersections and set differences
It can be shown that a σ-algebra is closed under intersections and set differences:
When are the concepts of partitions and sigma algebra’s equivalent
For finite sample spaces, the notions of partition and σ-algebra are equivalent.
What is a sigma algebra used for in probability theory? What is the smallest sigma algebra in the real numbers?
In probability theory, σ-algebra is used to represent a set of events. The smallest σ-algebra generated by intervals in R is called Borel σ-algebra.
Provide the necessary elements and definition of a probability space
The triplet (Ω, F, P) is then called a probability space.
Construct a sigma algebra over the natural numbers by considering odd and even figures
Give 3-5 properties of a probability measure
State the law of Total Probability
When are two events independent ?
Define ConditionaI probability and its central features
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