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PHP 2511 Distribution

memorize.ai (lvl 286)

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Section 1

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Discrete data

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Date created

Mar 1, 2020

Cards (13)

Section 1

(13 cards)

Discrete data

Front

Data that can only take certain values.

Back

Poisson distribution

Front

•Suppose that a hospital has observed 10 cases of a rare cancer of the past 20 years (0.5 cases per year). •Suddenly the hospital observes 3 cases in 1 year. How unusual is this given that the hospital treats about 25,000 patients a year. • •This story best fits a Poisson Distribution.

Back

Normal distribution

Front

a bell-shaped curve, describing the spread of a characteristic throughout a population •We call μ the mean of the normal distribution and σ the standard deviation. • •One Normal distribution that we will use a great deal in the future has a mean of 0 and a standard deviation of 1. • •We typically call this Z and Z~ N(0,1).

Back

Exponential distribution

Front

•We have that successes arrive at a rate of succeses per the time interval t. The average success rate for t is

Back

Continuous data

Front

• This is data that cannot be placed into a finite number of categories. It can take on any value.

Back

Hypergeometric distribution

Front

•If we have a population with h healthy people and u unhealthy people, then the probability of choosing an unhealthy person at random is u/(u+h) • • If we choose n people from this population with replacement then the distribution for the number of unhealthy people chosen in n trials is Bin (n, u/(u+h)). • •If we sample from this population without replacement then the number of unhealthy people follows a Hypergeometric Distribution. •, X~ Hgeom(u,h,n) • •The Hypergeometric however has dependent Bernoulli trials due to the fact that when you remove one success you change the probability of getting another success..

Back

Uniform distribution

Front

•A Uniform random variable on the interval (a,b) is a completely random number between a and b. • •In order for this to be completely random we specify that the PDF be a constant over that entire interval. • •We denote this by U~Unif(a,b).

Back

Binomial Distribution

Front

•Suppose you have n independent trials where the results of each trial are success or failure. • •Suppose further that the probability of a success is p and the probability of a failure is 1-p. • •Then the total number of successes is a binomial random variable with parameters n and p. • •The mean is np. • •The variance is np(1-p). that X~Bin(n,p)

Back

Geometric distribution

Front

•Think of this as the number of trials to get a single success.

Back

Ordinal Data

Front

categories can be arranged in a logical order from least to greatest

Back

Gamma distribution

Front

•The Gamma distribution is similar to the exponential distribution with the exception that rather than it being waiting time of the first success it represents the waiting time for multiple successes.

Back

Nominal data

Front

Other times there is no natural ordering and the data are just named categories.

Back

Bernoulli distribution

Front

The Bernoulli is the simplest probability distribution. It represents only 2 values, many times we just use 0 or 1. •We say that 1 is a success that happens with probability p. •The mean of this is p. •The variance is p(1-p). • •We would say X is distributed as Bernoulli(p) and write X~Bern(p). The number p is called the parameter of the distribution.

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