# Question

Suppose that f(x, t) is the probability of getting x successes during a time interval of length t when

(i) The probability of a success during a very small time interval from t to t + △t is α ∙ △t,

(ii) The probability of more than one success during such a time interval is negligible,

(iii) The probability of a success during such a time interval does not depend on what happened prior to time t.

(a) Show that under these conditions

And hence that

(i) The probability of a success during a very small time interval from t to t + △t is α ∙ △t,

(ii) The probability of more than one success during such a time interval is negligible,

(iii) The probability of a success during such a time interval does not depend on what happened prior to time t.

(a) Show that under these conditions

And hence that

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