Chapter 5 - Continuous Distributions Flashcards Preview

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

Probability density function

- measure of which values are more probable than others and to what degree
- analogous to the probability-mass function


Cumulative distribution function

- 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


Probability of individual values

- probability of individual values = 0


Normal distribution

- 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


The pdf of a normal distribution

- based on parameters of mean and standard deviation
- one standard deviation away from the mean represents the point of inflection


Standard normal distribution

- 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


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



- 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


Correlation coefficient

- 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


Bernoulli trial

- random variable that takes on the value 1 with probability p and the value 0 with probability q=1-p
- special case of a binomial random variable with n = 1