Random variables And probability Distributions

standard normal distribution

a normal distribution with μ=0 and σ=1

a standard normal distribution variable

a random variable with a standard normal distribution, denoted by the symbol z

probability distribution for a continuous random variable

a smooth curve called density function or frequency function. it is a function of x, denoted f(x). the probability that x falls between two values, a and b, is the area under the curve between a and b.

random variable

a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) numerical value is assigned to each sample point (4.1-P185)

binomial random variables

characteristics of a binomial experiment: 1. the experiment consists of n identical trails. 2. there are only two possible outcomes on each trial. 3. the probability of S remains the same from trial to trial. 4. trials are independent 5. the binomial random variable x is the number of S's in n trials 双等独 (4.3-P199) 经典事例：扔硬币

probability distribution

probability distribution of a discrete random variable is a graph, table, or formula that specifies the probability associated with each possible value the random variable can assume (4.2-P189)

discrete random variable

random variables that can assume a countable number ( finite or infinite) of values (4.1-P187)

continuous random variable

random variables that can assume values corresponding to any of the points contained in one or more intervals ( infinite and uncountable) (4.1-P187)

the binomial probability distribution

see Notes (4.3-P203)

normal random variable

the most common observed continuous random variables which have a bell-shaped curve.

mean, or expected value of a discrete random variable

μ=Ε(x)=Σxp(x) 加权平均数 (4.2-P191)

variance of a discrete random variable

σ2=Ε[(x-μ)2]=Σ(x-μ)2p(x)=Σx2p(x)-μ2 (4.2-P192)