SECTION 5 Week in Review 2011

# SECTION 5 Week in Review 2011 - Expected Value Variance...

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1 xp(x) x 2 p(x) **Remember to include UNITS! ** AEM 2100, Spring 2011 WEEK IN REVIEW February 28 – March 3 SECTION 5 Random Variable: A random variable, X, associates one and only one numerical value to each sample event of an experiment Two types: 1.Discrete (countable, how many times did the event happen?) 2.Continuous (measurable, can take on any values contained in one or more intervals of a line) Discrete Probability Distributions: The probability distribution of a discrete random variable “X” is a list of the distinct numerical values of “X” along with their associated probabilities, p(x) Example: A coin is tossed ten times. The random variable X is the number of tails that are noted. X can only take the values 0, 1, …, 10, so X is a discrete random variable (countable). Conditions for a Discrete Probability Function: 0 p(x) 1, for all “X” p(x) = 1, over all values of “X” Recommendation: set up a table with columns labeled: x p(x) xp(x) x 2 p(x)_ Expected Value, Variance, and Standard Deviation of a Discrete Random Variable:

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Unformatted text preview: Expected Value: Variance: Standard Deviation: Characteristics of the Binomial Random Variable: 1. The experiment consists of “n” identical trials . 2. There are only two possible outcomes on each trial. We refer to one outcome as a success (S) and the other as a failure (F). 3. The probability of a success remains the same from trial to trial ; it is denoted by “p”. The probability of failure, therefore, is “1-p”. 4. The trials are independent . 5. The binomial random variable “X” is the number of successes in “n” trials. Binomial Probability Function: x = 0, 1, 2,. .., n AEM 2100, Spring 2011 WEEK IN REVIEW February 28 – March 3 n = the number of trials p = the probability of success on one trial x = the number of successes in “n” trials Expected Value, Variance, and Standard Deviation of a Binomial Random Variable: Expected Value: Variance: Standard Deviation:...
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SECTION 5 Week in Review 2011 - Expected Value Variance...

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