Question 4.142

4.142 Some probability distributions.

Here is a probability distribution for a random variable :

Value of 2 3 4
Probability 0.2 0.4 0.4
  1. Find the mean and standard deviation for this distribution.
  2. Construct a different probability distribution with the same possible values, the same mean, and a larger standard deviation. Show your work and report the standard deviation of your new distribution.
  3. Construct a different probability distribution with the same possible values, the same mean, and a smaller standard deviation. Show your work and report the standard deviation of your new distribution.