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5_Discrete RVs_handouts

# 5_Discrete RVs_handouts - STAT 5615 Statistics in...

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1 STAT 5615 Statistics in Research (I) Discrete Random Variables Ott & Longnecker 4.6-4.8, 10.5 (before “tests using Poisson distribution”)

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2 Population Models Population - an unobservable realization of sample space - outcomes not equally represented - probability distribution describes the probability of each outcome in the population Random variable - outcome of a single draw from the population - also described by probability distribution - denoted by y in textbook
3 Probability Distributions Standard families of probability distributions Indexed by parameters : Each family describes a type of possible shapes for the population Parameters act as identify a specific probability distribution within the family Mean and standard deviation (or variance) of the population: two particular functions of the parameters

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4 Discrete Random Variables can assume a countable number of values Examples - gender of a cat: y = M or F. - number of students in STAT 5615 who still remember calculus: y = 0, 1, 2, …, 160. - number of security updates from Microsoft in the future: y = 0, 1, 2, 3, 4, 5, …
5 Probability Distributions for Discrete Random Variables Probability distribution for discrete r.v., also called probability mass function (PMF), lists the probability of obtaining each possible value. Probability mass function P( y ): for each possible value y , P( y ) is the probability of obtaining value y for the discrete r.v. P( y ) must satisfy the following conditions: 1) P( y ) lies between 0 and 1 2) Sum of probabilities for all values of y equals 1 3) P(y=y1 or y2) = P(y1) + P(y2)

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Continuous Random Variables can assume an uncountable number of values, e.g., all values on an interval Examples - weight gain of a person in the winter: y can be any values. - time to finish STAT 5615 final exam: 0 <
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5_Discrete RVs_handouts - STAT 5615 Statistics in...

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