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For the following distribution: x P(x) 0 0.12 1 0.27 2 0.31 3 0.08 4 0.22 a. Is this a valid probability distribution? Explain. b.

For the following distribution:

x

P(x)

0

0.12

1

0.27

2

0.31

3

0.08

4

0.22

a. Is this a valid probability distribution? Explain.

b. What is the expected value?

c. What is the variance of the distribution?

d. What is the probability that x is at least 3?

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