Question: Consider the following discrete probability distribution. x P(x) 1 0.25 2 0.30 3 0.45 Calculate the expected value, variance, and standard deviation of the random

  1. Consider the following discrete probability distribution.

x

P(x)

1

0.25

2

0.30

3

0.45

  1. Calculate the expected value, variance, and standard deviation of the random variable.
  2. Let y=x+5. Calculate the expected value, variance, and standard deviation of the new random variable.
  3. What is the effect of adding a constant to a random variable on the expected value, variance, and standard deviation?
  4. Let z=5x. Calculate the expected value, variance, and standard deviation of the new random variable.
  5. What is the effect of multiplying a random variable by a constant on the expected value, variance, and standard deviation?

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