Flashcards in Chapter 5 - Continuous Distributions Deck (10):

1

## Probability density function

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- measure of which values are more probable than others and to what degree

- analogous to the probability-mass function

2

## Cumulative distribution function

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- the cumulative distribution function for the random variable X evaluated at the point a is defined as the probability that X will take on values less than or equal to a

- represented by the area under the pdf to the left of a

3

## Probability of individual values

### - probability of individual values = 0

4

## Normal distribution

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- most widely used continuous distribution

- also called the Gaussian distribution

- other distributions that are not normal can be made approximately normal by transforming data onto a different scale

- any random variable that can be expressed as a sum of many other random variables can be well approximated by a normal distribution

5

## The pdf of a normal distribution

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- based on parameters of mean and standard deviation

- one standard deviation away from the mean represents the point of inflection

6

## Standard normal distribution

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- a normal distribution with mean 0 and variance 1

- about 68% of the area under the standard normal density lies between +1 and -1

- about 95% of the area lies between +2 and -2

- about 99% of the area lies between +2.5 and 2.5

7

## Properties of the standard normal distribution

### - a normal range for a biological quantity is often defined by a range within x standard deviations of the mean for some specified value of x

8

## Covariance

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- if X and Y are independent, then the covariance between them is 0

- if large values of X and Y occur among the same subjects (or small values of X and Y), then the covariance is positive

- if large values of X and small values of Y(or conversely, small values of X and large values of Y) tend to occur among the same subjects, then the covariance is negative

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## Correlation coefficient

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- dimensionless quantity that ranges between -1 and 1

- if X and Y are approximately linearly related, a correlation coefficient of 0 implies independence

- correlation close to 1 implies nearly perfect positive dependence

- correlation close to -1 implies nearly perfect negative dependence

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