Supposethat X is theoutcome of asingle Bernoullitrial, taking the value0or 1. Then X hasaBernoulliprobabilitydistribution, or Bernoulli distribution forshort.Ifwelet p denotethe probabilitythat X takesthe value1,then X is said to have aBernoulli distribution with parameter p.Since P (X =1)+P(X =0)=1, the probabilitymassfunction of X is P (X =1)=p(1)=p and P (X =0)=p(0)=1−p. Here, as usual, p() denotesthe p.m.f., butthe letter p is also used conventionally for the Bernoulli parameter. That is, p(x)= ) 1−px=0 px=1.
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