P (X = k) = (1-p) ^ (k-1) * p

In this equation, X embodies the random variable representing the count of trials, k stands for the count of trials required for the initial successful outcome, and p denotes the probability of success in a single trial.

Memorylessness: This distribution demonstrates memorylessness, meaning that the likelihood of success in future trials remains independent of the result of past trials.

Expectation and Variance: The expected value or mean of a Geometric Distribution equals 1/p, and the variance equates to (1-p) / p^2.

Skewness: The Geometric Distribution tends towards positive skewness, with the skewness rising in proportion to a decrease in the probability of success.

Reliability Engineering: The distribution contributes to modeling the count of trials necessary before a system failure takes place.

Quality Control: In manufacturing contexts, the Geometric Distribution can depict the count of items inspected before finding a defective one.

Biology: This distribution facilitates modeling the count of trials needed for a particular genetic event to appear in a population.

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