On distribution of waiting time for the first failure followed by a limited length success run
Many doctors believe that a patient will survive a heart attack unless a succeeding attack occurs in a week. Treating heart attacks as failures in Bernoulli trials we reduce the lifetime after a heart attack to the waiting time for the first failure followed by a success run shorter than a given $k$. In order to test the “true” critical period of the lifetime we need its distribution. The probability mass function and cumulative distribution function of the waiting time are expressed in explicit and concise form by binomial coefficients.