EXAM 2 FORMULA SHEET



Exam 2 Formula Sheet

CHAPTER 4

➢ [pic]

➢ If A and B are disjoint (mutually exclusive), [pic].

➢ If a random phenomenon has k possible outcomes, all equally likely, then each individual outcome has probability [pic].

➢ The probability of any even A is [pic].

➢ If A and B are independent, [pic].

➢ In the language of random variables, if X has the [pic] distribution, then the standardized variable [pic] is a standard normal random variable having the distribution [pic].

➢ Suppose that X is a discrete random variable whose distribution is

|Value of X |[pic] |

|Probability |[pic] |

The mean of X is: [pic]

The variance of X is: [pic]

➢ If events A, B, and C are disjoint (mutually exclusive), then [pic].

➢ For any two events A and B, [pic].

➢ The probability that both of two events A and B happen together can be found by [pic]. Here [pic] is the conditional probability that B occurs given the information in A occurs.

➢ When [pic], the conditional probability of B given A is [pic].

➢ Two events A and B that both have positive probability are independent if [pic].

Chapter 5

➢ If a count X has the binomial distribution [pic], then [pic].

➢ The number of ways of arranging k successes among n observations is given by the binomial coefficient [pic] for k = 0, 1, 2, …, n.

➢ If X has the binomial distribution [pic] with n observations and probability p of success on each observation, the possible values of X are 0, 1, 2,… , n. If k is any one of these values, the binomial probability is [pic].

➢ Let [pic] be the mean of an SRS of size n from a population having mean [pic] and standard deviation [pic]. The mean and standard deviation of [pic] are [pic].

➢ If a population has the [pic] distribution, then the sample mean [pic] of n impendent observations has the [pic] distribution.

Chapter 6

➢ The confidence interval for a population mean will have a specified margin of error m when the sample size is [pic].

Chapter 7

➢ When the standard deviation of a statistic is estimated from the data, the result is called the standard error of the statistic. The standard error of the sample mean is [pic].

➢ Suppose that an SRS of size n is drawn from a [pic] population. Then the one-sample t statistic [pic] has the t distribution with n – 1 degrees of freedom.

➢ Suppose that an SRS of size n is drawn from a population having unknown mean [pic]. A level C confidence interval for [pic] is [pic].

▪ [pic] is the point estimate

▪ [pic] is the margin of error

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