Final answer:
To find the CDF and PDF of the minimum, X (1), of a random sample from a geometric distribution, you can use the complement of the union of the events where each individual in the sample is greater than a certain value.
Step-by-step explanation:
To find the cumulative distribution function (CDF) and probability density function (PDF) of the minimum, X (1), of a random sample of size 10 from a geometric distribution with parameter p, we can use the fact that the minimum of a sample is equal to the complement of the union of the events where each individual in the sample is greater than a certain value.
The CDF of X (1) is given by
CDF(X (1)) = 1 - (1-p)^n
where n is the sample size.
The PDF of X (1) can be obtained by taking the derivative of the CDF.