Lesson 5 Random Variable and Probability Distribution

Lesson 5 Random Variable and Probability Distribution -...

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Random Variables and Probability Distributions Definitions: Random Variable is a function that associates a real number with each element in the sample space. Discrete Random Variable – a random variable which takes on a finite or countable number of values. Nondiscrete or Continuous Random Variable – is a random variable that takes on a non-countable or infinite number of values.
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Examples: 1. Classify the following random variables as discrete or continuous: a. The number of traffic accidents occurring at a certain intersection b. The volume of gasoline sold from a certain gasoline station c. Proportion of people who patronize a certain brand of clothing d. Shelf life of bread sold in the grocery e. Number of eggs laid each month by a hen f. Number of applicants in a certain University 2. Let W be a certain random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W.
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Discrete Probability Distribution The set of ordered pairs (x , f(x) ) is a probability function, probability mass function, or probability distribution of the discrete random variable X if , for each possible outcome x, 1. 2. 3. Note: 1. The cumulative distribution function F(x) of a discrete random variable X with probability distribution f(x) is 2. The graph of f(x) is a probability histogram. f ( x ) 0 f ( x ) = 1 x F ( x ) = P ( X x ) = f ( t ) , for - < t x x < P ( X = x ) = f ( x )
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Example An experiment consists of tossing 3 fair coins. Let X denotes the number number of tails which come up. With each sample point we can associate a number for X, a random variable. Find the probability function and the distribution function of X. Draw the probability histogram.
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Lesson 5 Random Variable and Probability Distribution -...

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