STAT211 Chapter Notes - Chapter 5: Poisson Distribution, Bernoulli Trial, Mutual Exclusivity
26 Jun 2018
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Chapter 5.1-5.8
Random Variable: A statistic, such as sample mean.
Discrete: Takes on countable number of possible values (whole numbers, can be
infinitely long).
Continuous: Takes on an infinite number of possible values (all R numbers).
Probability Distribution: For a discrete random variable X, is a listing of all possible values
of X and their probability of occurring.
Expectation: The theoretical mean of a random variable, or equivalently, the mean of its
probability distribution. A parameter.
E(X) = Σxp(x) u = E(X)
E(g(X)) = Σg(x)p(x)
Variance of a Discrete Variable: The theoretical variance for the probability distribution, a
parameter.
Var(X) = Σ(x-u)2p(x) o2 = Var(X)
Var(X) = E(x2) – [E(X)]2
E(a + bX) = a + bE(X)
Var(a + bX) = b2Var(X)
E(X – Y) = E(X) – E(Y)
E(X + Y) = E(X) + E(Y)
Var(X – Y) = Var(X) + Var(Y)
Var(X + Y) = Var(X) + Var(Y)
Bernoulli Distribution: P(X = x) = px(1 – p)1-x . Must have two mutually exclusive events
(success and failure) and 1 independent trial.
Binomial Distribution: The distribution of the number of successes in n independent
Bernoulli trials. P(X = x) = n!/x!(n-x)! * px(1 – p)n-x and u = np and o2 = np(1-p).
n = # trials
x = # desired successes
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Document Summary
Random variable: a statistic, such as sample mean. Discrete: takes on countable number of possible values (whole numbers, can be infinitely long). Continuous: takes on an infinite number of possible values (all r numbers). Probability distribution: for a discrete random variable x, is a listing of all possible values of x and their probability of occurring. Expectation: the theoretical mean of a random variable, or equivalently, the mean of its probability distribution. Variance of a discrete variable: the theoretical variance for the probability distribution, a parameter. Bernoulli distribution: p(x = x) = px(1 p)1-x . Must have two mutually exclusive events (success and failure) and 1 independent trial. Binomial distribution: the distribution of the number of successes in n independent. * px(1 p)n-x and u = np and o2 = np(1-p). n = # trials x = # desired successes p = probability of success.
