Statistics and Probability (Basic Probability (Estimation (An…
Statistics and Probability
The expected value of an experiment is the probability-weighted average of all possible values.
The law of large numbers states that the average result from a series of trials will converge to the expected value.
Probability is the measure of the likelihood that an event will occur
One of the main goals of statistics is to estimate unknown parameters.
An estimator uses measurements and properties of expectation to approximate these parameters.
An estimator's accuracy and precision is quantified by the following properties
difference between the estimator's expected value and the true value of the parameter being estimated.
It informally measures how accurate an estimator is.
Variance is the expectation of the squared deviation of an estimator from its expected value.
It informally measures how precise an estimator is.
Mean Squared Error
Mean squared error (MSE) of an estimator is the sum of the estimator's variance and bias squared.
Basic probability is an introduction to the foundational ideas in probability theory.
Compound probability is the probability of joint occurrence of two or more simple events.
Set Theory is a branch of mathematics concerned with the description and definition of sets, which are collections of objects.
In the context of probability theory, we use set notation to describe compound events.
Combinatorics is a branch of mathematics concerned with counting sequences and sets of objects.
Permutations represent unique orderings of objects in a set.
Combinations represent unique combinations of objects in a set.
Conditional probability is a measure of the probability of an event given another event has occurred.
A distribution is a mathematical description of a random variable's probability space.
A random variable is a mapping of a probability space to a set of real values.
Discrete and Continuous
A discrete random variable is a random variable that has countable values, such as a list of integers.
A continuous random variable is a random variable with a set of possible values that is infinite and uncountable, such as all real numbers.