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