11.1 Rand Vars Discr

# 11.1 Rand Vars Discr - Random Variables Example 1...

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1/5/10 Random Variables Example 1. Experiment: Roll 2 dice Let X be a random variable. X = the sum of the two dice. Example 2. Experiment: Toss 10 coins Let Y be a random variable

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1/5/10 Random Variables Experiment: Roll 2 dice Let X be a random variable. X = the sum of 1 2 3 4 11 12 (1,1 ) (1,2 ) (3,1 ) (2,6 ) (2,1 ) (3,6 ) (6,6 )
1/5/10 Properties of Random Property 1 After an experiment is conducted and the outcome is observed, the random variable takes on a numerical value. The outcome of a random variable is a number . Example Suppose we select a random student

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1/5/10 Properties of Random Property 2 All random variables (X) have an associated “domain which is the set of all possible outcomes for X. In Example 1 above where 2 dice are rolled and X= their sum, the domain of X is {1,2,3,. ..,11,12} right?
1/5/10 Properties of Random Property 3 X has a probability distribution function which assigns a probability to each element of the domain. Probability Distributions are the most important concept to understand in Prob and Stats.

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1/5/10 Random Variables Experiment: Roll 2 dice Let X be a random variable. X = the sum of 1 2 3 4 11 12 (1,1 ) (1,2 ) (3,1 ) (2,6 ) (2,1 ) (3,6 ) (6,6 )
1/5/10 Types of R.V.’s The book tends to use the following notation: Let f(x) be the probability distribution function of random variable X. I will try to use the more precise notation and definitions: Discrete Random Variables are random

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1/5/10 Probability Mass Functions As stated above, PMF’s assign a probability to each element of the domain of a random variable. Thus fX(x) means P(X=x) for values x
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11.1 Rand Vars Discr - Random Variables Example 1...

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