lecture_02 - Probability Distributions for Qualitative Data...

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ILRST 411 - Lecture  02  Probability Distributions for  Qualitative Data
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          Key Distributions for Categorical Data For Regression and Analysis of Variance (ANOVA)  models for  continuous data the normal distribution plays a key role. For  Categorical data analysis , two key distributions,  Poisson  and  Binomial  play a key role. We will cover:        Binomial  distribution       Poisson  distribution       Multinomial   distribution       Hypergeometric  distribution
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    Random Variable Random Variable : A random variable is a measured  quantity associated with a random phenomenon Random variables are denoted by a capital letter such  as  or  Y Example:  Toss three coins and consider the number of heads  out of the three tosses. The number of heads in three  tosses is a random variable that can take values 0, 1,  2, or 3.      
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    Probability Distributions The  probability distribution  for a random variable tells the  possible values of the random variable and the probability  associated with the values or interval of the values. The probability distribution for a  discrete  random variable is  called the  probability mass function , because it tells how  much of the mass of the unit of probability is at each specific  value. continuous  random variable has probability on intervals  of values, not on specific values.The probability distribution  for a continuous random variable is called  probability  density function.
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            Binomial   Distribution  There are many applied problems in which we are  interested in the probabilities that an event will occur  x   times out of  n . Examples:  - Probability of getting 5 heads in 12 flips of a coin - Probability that 7 of 10 persons will recover from a            tropical disease - Probability that 35 of 80 persons will respond to a mail           order solicitation
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            Binomial Distribution  -  Assumptions 1. There is a  fixed number of trials , each scored as  success or failure 1. The  probability of a success is the same  for  each trial. ( example – heads or tails ) 1. The trials are all  independent  ( If we toss a coin 2  times the outcome of one trial does not depend on the  other trial )
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    Binomial Distribution -  Probabilities The possible values of the binomial random variable are  integer values from 0 to n.
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