I completely forgot about the knowledge of probability theory QAQ
1.PDF: If X is a continuous random variable, define the probability density function as f The probability of , that is
[only continuous types have]
CDF: No matter what type of random variable (continuous/discrete/other), its cumulative distribution function can be defined, sometimes referred to as the distribution function.
Continuous type:
CDF is the integral of PDF, and PDF is the derivative of CDF.
Discrete: Discrete random variable, its CDF is a piecewise function, such as the random variable of coin toss in the example, its CDF is:
For discrete random variables, distribution laws can be used directly to describe their statistical regularity; for continuous random variables (non-discrete random variables), we cannot list all possible values of the random variables, so its Probability distributions cannot be described by distribution laws like discrete random variables. So PDF was introduced and integral was used to find the probability of a random variable falling into a certain interval.
F ( x ) F ( x ) The function value of F(x) at point x xx represents the probability that X XX falls within the interval ( − ∞ , x ] (−\infty,x](−∞,x], so The distribution function is an ordinary function whose domain is R RR. Therefore, we can transform the probability problem into a function problem, so that we can use ordinary function knowledge to study probability problems, which increases the scope of probability research. The above is excerpted from PDF in
Probability Theory , the difference and connection between PMF and CDF
2. The following is excerpted from the calculation and meaning of the covariance matrix
Covariance: Definition:
Covariance (i, j) = (all elements in the i-th column - mean of the i-th column) * (j-th column All elements of the column - the mean of the jth column)
The meaning of covariance is to find the correlation between dimensions.
Covariance matrix:
3. The joint probability of A and B is expressed as P(AB) or P(A,B), Or P (A∩B)
can be deduced
4. Excerpted from the simple understanding of the meaning of the semicolon in the function f (x; θ)
f (x; θ), the actual meaning is f (x), but it is emphasized that the parameters of the function are θ