Which of the following is not a required condition for the distribution of a discrete random variable X that can assume values x_i? A) 0 $\le$ p(x_i)$\le$ 1 for all x_i B) $$\sum _ { \text {all } x _ { 1 } } p \left( x _ { i } \right) = 1$$ C) p(x_i) 1 for all x_i D) All of these choices are true.

Question

Which of the following is not a required condition for the distribution of a discrete random variable X that can assume values x_i? A) 0 $\le$ p(x_i)$\le$ 1 for all x_i B) $$\sum _ { \text {all } x _ { 1 } } p \left( x _ { i } \right) = 1$$ C) p(x_i)> 1 for all x_i D) All of these choices are true.

Quizplus · Accepted Answer

The condition p(x) > 1 for all x is not a required condition for the distribution of a discrete random variable. This condition is impossible to meet as probabilities must be between 0 and 1, inclusive. The other conditions, that the probabilities must be non-negative (0 ≤ p(x) ≤ 1), that the sum of all probabilities must equal 1, and that the probabilities must be defined for all possible values of x, are required conditions for a valid probability distribution.

Which of the Following Is Not a Required Condition for the Distribution