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# MATH 153 Chapter 6

### Discrete & Binomial Probability Distributions

Question | Answer |
---|---|

True/False -1 </= P(x) </= +1 | False |

Binomial experiment | Experiment that: has two possible mutually exclusive outcomes (success or failure); has a fixed number n of trials; trials are independent of each other; and probability of success, P(success), will be the same for each trial |

Success | Outcome (in a binomial experiment) that has been defined as desirable or that is being studied |

Failure | Any outcome (in a binomial experiment) that is not defined as a success |

Random variable | Numerical value of the outcomes of a probability experiment (typically written as X). |

Discrete random variable | Random variable that has a finite or countable number of values. For example, the outcomes of a coin toss |

Continuous random variable | Random variable that has an infinite number of values. For example, a person’s height |

Probability distribution | A table with all possible values of outcome X along with the probabilities of each outcome P(x). The sum of all probabilities is equal to 1 (Σ P(x) = 1), and the probability of each outcome is between 0 and 1 (0 ≤ P(x) ≤ 1) |

Mean of a discrete random variable | The expected value of a discrete random variable. It is equal to the sum of the value of each random variable times the probability of that outcome (μx = Σ x P(x)) |

Expected value | The mean of a discrete random variable, or in other words, what is expected to be the average outcome of an experiment in the “long run” |

What is the sum of all probabilities in a discrete probability distribution | 1 |

True/False As the number of trails increases in a binomial experiment, the probability distribution becomes less bell-shaped. | False |

What does 1-p in a binomial experiment represent? | Probability of failure |

In a binomial probability distribution, what percentage of observations does μ − 2σ and μ + 2σ represent. | 95% |

True or false: As n increases, the binomial distribution becomes more bell shaped. | True |

What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? | E(X)=np |

True or false: In the binomial probability distribution function, nCx represents the number of ways of obtaining x successes in n trials. | True |

A __________________________ is a numerical measure of the outcome of a probability experiment. | random variable |

An ______ compound event is generally associated with multiplication; an ______ compound event is generally associated with addition. | AND, OR |

What method of assigning probabilities to a simple event uses relative frequencies? a. Subjective b. Classical c. Empirical | c. Empirical |

True or false: In a combination problem, order is not important. | True |

A _______________ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order. | combination |

A(n) ________________ is an ordered arrangement of r objects chosen from n distinct objects without | permutation |

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