Starnes, UPDATED The Practice of Statistics, 6e, Chapter 6

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random variable

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17 Terms

1

random variable

Takes numerical values that describe the outcomes of a random process.

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2

probability distribution

Of a random variable, gives its possible values and their probabilities.

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3

discrete random variable

χ takes a fixed set of possible values with gaps between them.

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4

mean (expected value) of a discrete random variable

Its average value over many, many trials of the same random process.

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5

standard deviation of a discrete random variable

Measures how much the values of the variable typically vary from the mean in many, many trials of the random process.

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6

variance

The weighted average of squared deviations.

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7

continuous random variable

Can take any value in an interval on the number line.

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8

independent random variables

If knowing the value of χ does not help us predict the value of γ, then χ and γ are "independent random variables". In other words, two random variables are independent if knowing the value of one variable does not change the probability distribution of the other variable.

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9

binomial setting

Arises when we perform 𝑛 independent trials of the same random process and count the number of times that a particular outcome (called a “success”) occurs. The four conditions for a binomial setting are: i) Binary? The possible outcomes of each trial can be classified as “success” or “failure.”; ii) Independent? Trials must be independent. That is, knowing the outcome of one trial must not tell us anything about the outcome of any other trial.; iii) Number? The number of trials 𝑛 of the random process must be fixed in advance.; iv) Same probability? There is the same probability of success p on each trial.

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10

binomial random variable

The count of successes χ in a binomial setting. The possible values of χ are 0, 1, 2, …, n.

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11

binomial distribution

The probability distribution of χ. Any "binomial distribution" is completely specified by two numbers: the number of trials 𝑛 of the random process and the probability p of success on each trial.

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12

binomial coefficient

The count of the number of arrangements of x successes in 𝑛 trials.

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13

10% condition

When taking a random sample of size 𝑛 from a population of size 𝑁, we can treat individual observations as independent when performing calculations as long as 𝑛 < 0.10𝑁.

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14

Large Counts condition

Suppose that a count χ of successes has the binomial distribution with 𝑛 trials and success probability 𝑝. The "Large Counts condition" says that the probability distribution of χ is approximately Normal if 𝑛𝑝≥10 and 𝑛(1−𝑝)≥10. That is, the expected numbers (counts) of successes and failures are both at least 10.

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15

geometric setting

Arises when we perform independent trials of the same random process and record the number of trials it takes to get one success. On each trial, the probability p of success must be the same.

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16

geometric random variable

The number of trials χ that it takes to get a success in a geometric setting.

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17

geometric distribution

The probability distribution of χ is a "geometric distribution" with probability 𝑝 of success on any trial. The possible values of χ are 1, 2, 3, . . . .

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