Common probability distributions including binomial, normal, and Poisson, with their defining properties and typical uses.
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- What is the binomial distribution used to model?
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The number of successes in a fixed number of independent trials, each with the same probability of success.- What are the two parameters of a binomial distribution?
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n (number of trials) and p (probability of success on each trial).- What is the probability mass function of a binomial distribution?
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P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where C(n,k) is the binomial coefficient.- What is the mean of a binomial distribution with parameters n and p?
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np- What is the variance of a binomial distribution with parameters n and p?
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np(1-p)- Give a real-world example of a binomial distribution.
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The number of heads in 20 coin flips, or the number of defective items in a batch of 100 products.- When n is large and p is small, the binomial distribution can be approximated by which distribution?
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The Poisson distribution.- What is the range of possible values for X in a binomial distribution?
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X can be 0, 1, 2, ..., n (integer values from 0 to n).- What is the normal distribution also called?
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The Gaussian distribution.- What are the two parameters of a normal distribution?
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mu (mean) and sigma (standard deviation).- What is the mean of the standard normal distribution?
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0- What is the standard deviation of the standard normal distribution?
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1- What is the probability density function for a normal distribution?
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f(x) = (1/(sigma*sqrt(2*pi))) * exp(-(x-mu)^2/(2*sigma^2))- What percentage of data falls within one standard deviation of the mean in a normal distribution?
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Approximately 68%.- What percentage of data falls within two standard deviations of the mean in a normal distribution?
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Approximately 95%.
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