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)