However, if we break down one minute into 60 seconds, it is likely that only one car passes or no car pass in a single second. For a minute, maybe more than one cars pass the street, thus it is not a binary random variable. To understand the car passing event, you can break down one hour into 60 minutes, and see how many cars will pass in a minute, then generalize it into an hour. For example, when measuring how many cars will pass a particular street in an hour, the number of cars passing is a random variable that follows Poisson distribution. Poisson distribution is closely related to binomial distribution if you measure the number of event occurrences as the number of success. Poisson distribution can be used to present the number of customers arriving in a store in an hour, or the number of phone calls a company receives one day, etc. Poisson distribution is a discrete distribution that models the probability of a number of events occurring in a fixed interval of time or space. Normal Distribution by CLM 6, Poisson Distribution The PMF is defined using the combination formula: There are two parameters in the distribution, the success probability p and the number of trials n. ![]() ![]() The assumptions of the Binomial distribution are:ġ, each trial only has two outcomes (like tossing a coin) Ģ, there are n identical trials in total (tossing the same coin for n times) ģ, each trial is independent of other trials (getting “Head” at the first trial wouldn’t affect the chance of getting “Head” at the second trial) Ĥ, p, and 1-p are the same for all trials (the chance of getting “Head” is the same across all trials) You can think of the binomial distribution as the outcome distribution of n identical Bernoulli distributed random variables. Simulating a Bernoulli trial is straightforward by defining a random variable that only generates two outcomes with a certain “success” probability p: import numpy as np #success probability is the same as failure probability np.random.choice(, p=(0.5, 0.5)) #probabilities are different np.random.choice(, p=(0.9, 0.1)) 2, Binomial Distributionīinomial distribution is also a discrete distribution, and it describes the random variable x as the number of success in n Bernoulli trials.
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