# week3 - Statistics 511 Random Variables and Probability...

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1 Statistics 511 Random Variables and Probability Distributions Relevant Sections: 4.6 – 4.8 (4.6) Variables Random variable a. Qualitative b. Quantitative 1. Discrete 2. Continuous (4.7) Discrete Random Variables Probability distribution of Y – gives the possible values of Y (denoted by y) and corresponding probabilities P(y). Ex. Y = the number of heads when 2 coins are tossed. What is P(y)? Properties

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2 (4.8) Binomial Random Variable/ Probability Distribution Characteristics: P(y) = Mean: Standard deviation: Ex. Suppose that a woman plans to have 5 children. Suppose also that the probability of a boy is .51 at each birth and the sexes of successive children are independent. Find the following probabilities: a. None of the children are boys b. There are exactly 3 boys c. There are at least 2 boys d. All of the 5 children are boys
3 Statistics 511 Relevant Sections: 4.9 – 4.10 (4.9) Continuous Random Variables and Probability Distributions f(y) Graphical representations: Total area under the curve P(a < y <b) Important notes: (4.10) Normal Distribution Normal probability (density) function:

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4 Common notation: Standard normal random variable See Table 1 on pp1091 – 1092 Standardization:
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week3 - Statistics 511 Random Variables and Probability...

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