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 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

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

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

A discrete random variable X has this probability distribution.a) Complete the table (10 pts)Compute:b) 𝜇 = 𝐸(𝑋) = ∑[𝑥𝑃(𝑥)] = ___________________ (2 points)c) 𝑉𝑎𝑟(𝑋) = ∑[(𝑥 − 𝜇)2𝑃(𝑥)] = ___________________ (2 points)d) Standard deviation. ___________________ (1 points)Note: Answers from b – d, round off to 2 decimal places. For the table take all decimal places.𝑥 0 1 2 3 4𝑃(𝑥) 0.12 0.25 0.18 0.35 0.10𝑥𝑃(𝑥)𝑥 − 𝜇(𝑥 − 𝜇)2(𝑥 − 𝜇)2𝑃(𝑥)

The P(X ≤ x) is an example of a cumulative probability.Group of answer choicesTrueFalse