Properties of a Probability Distribution

Question

Determine whether this represents a valid discrete probability distribution. If not, explain why.

x P(X=x)

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-22 0.4

53 1.05

-15 0.05

Answer 1

A probability distribution must satisfy two conditions: first, the sum of all possible probabilities must equal 1. Since 0.4 + 1.05 + 0.05 = 1.5, this is not a valid probability distribution.

Additionally, all possible probabilities must be between 0 and 1, so since P(X=53) = 1.05, this is not a valid probability distribution.