Question

As the probability increases in a GEOMETRIC distribution, what happens to the mean, standard deviation, and shape of the distribution?

Answer 1

In a geometric distribution, as the probability increases, the mean and standard deviation decrease, and the shape of the distribution becomes more skewed towards smaller values.

Step-by-step explanation:

The mean, standard deviation, and shape of a geometric distribution are influenced by the probability.

If the probability increases in a geometric distribution:

1. The mean decreases.
2. The standard deviation decreases.
3. The shape of the distribution becomes more skewed towards smaller values.

For example, if the probability of success in a single trial increases, the expected number of trials until the first success decreases, resulting in a lower mean. Similarly, with a higher probability of success, the outcomes become more predictable, leading to a smaller standard deviation.