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Chap 3 - Common Univariate Random Variables - Coggle Diagram
Chap 3 - Common Univariate Random Variables
Uniform, Bernoulli, Binomial and Poisson Distributions
The Uniform Distribution
The continuous uniform Distribution
defined over a range (a ,b)
The Bernoulli Distribution
has 2 possible outcomes (failure success)
used for assessing the probability of binary outcomes
The Binominal Distribution
n independent Bernoulli trials
defines the probability of x success in n trials
The Poisson Distribution
X: the number of successes per unit
λ : the average number of successes per unit
Normal and Lognormal Distributions
The Normal Distribution
The normal Distribution
The confidence interval (khoảng tin cậy)
Range of values around E[x]
chính xác trong 1 khoảng thời gian
2 parameters: Mean, variance (standard deviation)
Key properties
X ~ N(μ, σ2)
Skewness = 0
Kurtosis = 3
The Standard Normal Distribution (Z-Distribution)
mean: 0; standard deviation: 1
z-value: độ lệch chuẩn giữa 1 giá trị quan sát (observation) và population mean
Calculating probabilities using z-values
F(Z)
The Lognormal Distribution
skewed to the right
bounded by 0 (always >=0)
Students's T, Chi-Squared, F-Disttributions
Student's t-Distribution
Definition
Small samples (n<30); unknown variance
Similar to Normal Distribution; fatter tails
defined by 1 parameter
Properties
symmetrical
defined by df; df = number of sample -1 = (n - 1)
fatter tails than normal distribution (greater probaility in the tails)
df increases => t-distribution looks more and more like to standard normal distribution
The Chi-Squared Distribution
used for hypothesis tests concerning the variance of a normal distributed population
asymetrical
bounded below by 0
The F-Distribution
used for hypothesis tests concerning the quality of the variances of 2 populations
right-skewed
being truncated at zero on the left-hand side
defined by 2 separate df
Key Properties
Others
Mixture Distributions