Continuous Probability Distribution
Basic Concept
Unlike discrets probability distribution, continuous probability distribution is continuous. The variables of the former can only be integers, while the latter is the entire field of real numbers.
Similar to discrete notation, the probability is usually written as
Note that, as with a discrete probability distribution, for a continuous probability distribution, the sum of all its events must be 1, i.e
This is often used as a way of checking whether a probability distribution is valid.
We usually write the Probability distribution function as
According to the Probability distribution function, We get the Cumulative distribution function:
Expactation:
Varience:
Median:
Mode: where the probability distribution has a maximum
Normal Distribution
Symbol:
Definition:
It is important to note that for this function, its integral (i.e., Cumulative distribution function) cannot be expressed as an elementary function. The questions usually give, for example,
Facts:
For a normal distribution, its mode is
(that is, the x value corresponding to the highest point of the image), and the function image is symmetric along .If
(Notes: is Binomial distribution), and n is “large”, p is “close to” 1/2, then can be approximated as a normal distribution (类似于“抛硬币”).If
(Notes: is Poisson distribution), and is large, the can be approximated by a normal distribution .
Continuous Probability Distribution
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