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Chapter 6 (Sp11)

# Chapter 6 (Sp11) - Section 6.1 Discrete Random Variables...

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Section 6.1 – Discrete Random Variables Random Variable – A numerical measure of the outcome of a probability experiment whose value is determined by chance. Generally denoted with capital letters (X). Discrete Random Variable – A random variable with a finite or countable number of values. The values can be plotted on a number line with space between each point. Ex : The number of students who ate pizza yesterday Continuous Random Variable – A random variable with infinitely many values. The values can be plotted on a number line in an uninterrupted fashion. Ex : The weight of a coin; speed of a car Probability Distribution – A graph, table, or formula that gives values of the random variable along with their corresponding probabilities. Requirements : ) ( x P = ______ ____ P( x ) ____ Probability Histogram – A histogram where the value of the random variable is plotted on the horizontal axis and the probability of each value of the random variable is plotted on the vertical axis. Example : Flip a coin 3 times. Let x = the # of heads x P( x ) Example : Create a probability histogram for the above example. 1

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Example : Is P( x ) = 4 x ( x = 1, 2, 3) a probability distribution? Mean and Standard Deviation of a Probability Distribution: ( 29 = ) ( x P x μ “sum of each x times its probability” ( 29 - = 2 2 ) ( μ σ x P x “square x , multiply by its probability then sum. Then subtract μ 2 Interpretation of the mean : The mean outcome of the experiment if we repeated the experiment multiple times. Interpretation of the standard deviation : How much the values deviate from the mean. Example : Find the missing probability, then calculate μ and σ : x P( x ) 0 0.3 1 0.5 2 3 0.08 μ = σ = 2
On the calculator: Enter the x values in L 1 Enter the P( x ) values in L 2 STAT, CALC, 1-Var Stats(L 1 , L 2 ) Example : X-linked Genetic Disorder Three males with an X-linked genetic disorder each have one child.

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Chapter 6 (Sp11) - Section 6.1 Discrete Random Variables...

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