Which of the following is a required condition for a discrete probability function?Question 2Select one:a.f(x) < 0 for all values of xb.ΣΣf(x) = 1 for all values of xc.ΣΣf(x) = 0 for all values of xd.f(x)   ≥≥1 for all values of x

Select all that applyWhich of the following are key properties of the discrete probability distribution?Multiple select question.The probabilities of success and failure remain the same from trial to trialThe probability of each value x is a value between 0 and 1, or, equivalently, 0 ≤ P(X = x) ≤ 1The number of successes within a specified time or space interval equals any integer between zero and infinityThe sum of the probabilities equals 1. In other words, ΣP(X = xi) = 1, where the sum extends over all values x of X

Which of the is not true for a discrete random variable X?*Option 4Option 1Option 3

In a probability distribution, ΣP(X=x) =__________Question 3Answera.0b.0 to +1c.-1 to +1d.1

Which of the following is not a characteristic of a probability density function f(x)?Multiple Choicef(x) becomes zero or approaches zero if x increases to +infinity or decreases to −infinity.f(x) is symmetric around the mean.The area under f(x) over all values of x equals one.f(x) ≥ 0 for all values of x.

A discrete random variable X has the probability distribution shown in the table belowDetermine the value of the constant a