4.130 Some probability distributions. Here is a probability distribution for a random variable X:

Value of X 2 3 4
Probability 0.4 0.3 0.3

  1. (a) Find the mean and standard deviation for this distribution.

  2. (b) 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. (c) Construct a different probability distribution with the same possible values, the same mean, and a smaller standard deviation. Show your work and report the stan- dard deviation of your new distribution.