By Miroslav Kaps
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Characteristics of a binomial experiment are: 1) The experiment consists of n equivalent trials, independent of each other 2) There are only two possible outcomes of a single trial, denoted with Y (yes) and N (no) or equivalently 1 and 0 3) The probability of obtaining Y is the same from trial to trial, denoted with p. The probability of N is denoted with q, so p + q = 1 4) The random variable y is the number of successes (Y) in the total of n trials. ,n where: p = the probability of success in a single trial q = 1 – p = the probability of failure in a single trial The expectation and variance of a binomial variable are: E(y) = µ = np Var(y) = σ2 = npq and The shape of the distribution depends on the parameter p.
The normal curve has the shape of a bell, and 38 Biostatistics for Animal Science its location and form are determined by two parameters, the mean µ and variance σ2. 14.. The following describe a variable y as a normal random variable: y ∼ N (µ, σ2) The parameters µ and σ2 are the mean and variance of the distribution. Recall, that the standard deviation is: σ = σ2 and represents the mean deviation of values from the mean. e. (f(µ) = maximum). That indicates that the mode and median are equal to the mean.
Similarly, the probability that the first is black and the second is spotted is: P[black ∩ (spotted | black)] = (2/10) (5/9) = 1/9 Since we are looking for a pair (black, spotted) regardless of the order, then we have either (spotted, black) or (black, spotted) event. 4 Bayes Theorem Bayes theorem is useful for stating the probability of some event A if there is information about the probability of some event E that happened after the event A. Bayes theorem is applied to an experiment that occurs in two or more steps.