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Sunil Barran

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Discrete random variables Definitions: • a random variable is a variable whose value is determined by the outcome of a random experiment • a random variable that assumes countable values is called a discrete random variable • a random variable that assumes any value contained in one or more intervals is called a continuous random variable Example: # fish in a lake; points scored in a football game; weight of a rhino; Definition: the probability distribution of a discrete random variable, x, lists all the possible values that the random variable can assume and their corresponding probabilities, p(x) Example: Suppose of 60% of all STATS151 students suffer from math anxiety. Two students are randomly selected. Let x denote the number of students in the sample who suffer from math anxiety. Construct the probability distribution of x. S= x p(x) 0 0.16 1 0.48 2 0.36 Sum= Find : P(x >1) ; P(x 1); First student Second student Final outcomes Y 0.6 YY=0.6*0.6=0.36 0.6 0.4 Y YN=0.6*0.4=0.2 N 4 0.6 NY=0.4*0.6=.0.2 0.4 Y 4 N 0.4 NN=0.4*0.4=0.1 N 6 Example: Space Shuttles. The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its Web site. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 1981 to July 2000. Let X denote the crew size of a randomly selected shuttle mission between April 1981 and July 2000. a. What are the possible values of the random variable X? b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7. c. Find P(X = 4); interpret in terms of percentages. d. Obtain the probability distribution of X. e. Construct a probability histogram for X. Mean of a discrete random variable x is the value that is expected to occur per repetition, i.e. on average if an experiment is repeated a large number of times. μ = E(x) = ∑ xP(x) 2 2 σ = ∑ x P(x) − μ Where is the standard deviation, measures the spread of the probability distribution. Example: An instant lott
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