Some probability distributions. Here is a probability distribution for a random variable X: Value of X: 2, 3, 4 Probability: 0.2, 0.4, 0.4 (a) Find the mean and standard deviation for this distribution. (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. (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 standard deviation of your new distribution. c