Question: Some probability distributions. Here is a probability distribution for a random variable X: Value of X 1 2 3 Probability 0.2 0.6 0.2 (a) Find

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

Value of X 1 2 3 Probability 0.2 0.6 0.2

(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.

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