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# MATH 153 Chapter 6

### Discrete & Binomial Probability Distributions

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