Random
Variables
Variables
The type variable that takes a fixed set of possible values with gaps between. The probability distribution of a ______________________ gives its possible values and their probabilities.
What is a discrete random variable?
In a binomial setting, suppose we let X = the number of successes. X has a _________________ distribution.
What is a binomial distribution?
When taking an SRS of size n from a population of size N, check that n > 0.10N.
What is the 10% condition?
P(X) = nCx px(1-p)n-x
What is the Binomial Probability Formula?
Variable that takes numerical values that describe the outcomes of some chance process.
What is a random variable?
Variable that can take any value in an interval on the number line. The probability distribution of a ___________________ is described by a density curve.
What is a continuous random variable?
Gives the possible values of a random variable and their probabilities.
What is a probability distribution?
Suppose that a count X of successes has the binomial distribution with n trials and success probability p. If np ≥ 10 and n(1 - p) ≥ 10, we can use __________________________.
What is the Normal approximation for a binomial distribution?
Square root of the variance of a discrete random variable. The ______________ measures the typical distance of the values in a distribution from their mean.
What is the standard deviation of a discrete random variable?
A situation is said to be this, if: Each observation either a success or failure.All observations are INDEPENDENT.The probability of success (p), is the SAME for each observation. There are a fixed number of trials.
What is a binomial setting?
The count X of successes in a binomial setting. The possible values of X are 0, 1, 2, ..., n.
What is a binomial random variable?
Suppose we let Y = the number of trials it takes to get a success. Y has a ________________ distribution.
What is a geometric distribution?
Suppose X is the number of successes and p̂ is the proportion of successes in a random sample of size n from a population with proportion of successes p. The _______________ says that the distribution of X and the distribution of p̂ will be approximately Normal if np ≥ 10 and n(1 - p) ≥ 10.
What is the Large Counts condition?
Weighted average of the squared deviations of the values of the variable from their mean.
What is the variance of a discrete random variable?
A situation is said to be this, if: Each observation either a success or failure.All observations are INDEPENDENT.The probability of success (p), is the SAME for each observation.The variable of interest is the number of trials required to obtain the FIRST success.
What is a geometric setting?
The number of trials Y that it takes to get a success in a geometric setting.
What is a geometric random variable?
What is a Normal distribution?
This rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean
The Empirical Rule
Describes the variable's long-run average value over many, many repetitions of the same chance process. μx = E(X) = x₁p₁ +x₂p₂ +x₃p₃ +... = σxipi
What is the mean (expected value) of a discrete random variable?
Pattern of inaccurate responses that could be due to wording, interviewer, lying, etc.
What is response bias?
If knowing the value of X does not help us predict the value of Y, then X and Y are ____________________________
What are independent random variables?
Geometric distributions always have this shape
What is right skewed?
This is the name of Mrs. Winfield's dog
What is Rey?
If Y has the geometric distribution with probability p of success on each trial, the possible values of Y are 1, 2, 3, .... If k is any one of these values, use this formula P(Y = k) = (1 - p)^(k - 1)p.
What is the geometric probability formula?
YES
Can Joy smell Parkinson's?