Final answer:
The question involves calculating the cumulative distribution functions for a Binomial(3,0.5) distribution and a Geometric(p) distribution on the set {1,2,...}. The CDF of the binomial distribution is obtained by summing up the probabilities of outcomes from 0 to x, while the CDF of the geometric distribution is the sum of probabilities from 1 to x trials.
Step-by-step explanation:
The question asks to find the cumulative distribution functions (CDF) for two different types of probability distributions: Binomial and Geometric. For a Binomial(3,0.5) distribution, the CDF at a value x would be the sum of the probabilities of getting 0, 1, 2, or 3 successes out of 3 trials when the probability of success on any given trial is 0.5. Thus, we would calculate the probabilities using the binomial formula and then add them up accordingly for each x.
For the Geometric (p) distribution on {1,2,…}, the CDF is the sum of the probabilities for all values from 1 to x, which involves a simple series summation. Geometric distribution models the number of trials needed to get the first success, and therefore, the CDF at a value x is the probability that the first success occurs on or before the x-th trial.