Consider the following discrete probability distribution:
x P(x)
5â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..0.10
10â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..0.15
15â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..0.25
20â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..0.50
a. Calculate the expected value of the random variable.
b. Let y = x + 5. Calculate the expected value of the new random variable y.
c. Let z = 5 x. Calculate the expected value of the new random variable z.
d. From your calculations in part a and part b, indicate the effect that adding a constant to a random variable has on the expected value of the random variable.
e. From your calculations in part a and part c, indicate the effect that multiplying a random variable by a constant has on the expected value of the random variable. |

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