The four conditions required for using a Binomial distribution are (a) A fixed n

Question

The four conditions required for using a Binomial distribution are (a) A fixed number of trials (n). Trials can be the repeat of a process (like flipping a coin) the re peat of an experiment (like giving a person a dr ug to treat a discase), or the repcat of a sampling process (like randomly sampling n people from a large population). (b) On cach trial, there are two possible outcomes, one of which we call a "success" (c) On each trial, Pr(success) is the same (d) The outcomes of each trial are independent For each of the following decide if the random variable defined (X) is a Binomial variable or not. It Is not a Blnom tions are not met. If It Is a Binomial, give the probability function, ial variable, say which of the four condi rl

Explanation / Answer

a) Here x is number of dead batteries and follows Binomial distribution with parameters n = 5, pi = 10/100 = 0.1

p[x] = 5Cx 0.1x 0.95-x

b) Here 'X' is the number of employed people with parameters n = 10, pi = 0.05

p [x] = 10Cx 0.05x 0.9510 - x

c) Here 'X' is the number of unemployed people with parameters n = 5, pi = 0.05

p [x] = 5Cx 0.05x 0.955 - x

d) Here 'X' is the number rolls of six sided die, n = infinite, p = 1/6

in this case, X follows poisson distribution which is the extension to the binomial,

i.e if n tends to infinite then poisson is limiting case of binomial

p [x] =

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