PMF PMF Properties and Axioms

Question 1

Which two conditions must every valid PMF satisfy?

Accepted Answer

P(X=x) ≥ 0 for all x, and Σ P(X=x) = 1

Answer

P(X=x) > 0 for all x, and Σ P(X=x) = 1

Answer

P(X=x) ≥ 0 for all x, and Σ P(X=x) ≤ 1

Answer

0 < P(X=x) < 1 for all x

Question 2

Which of the following is NOT a valid PMF for X ∈ {1, 2, 3}?

Accepted Answer

P(1)=0.4, P(2)=0.4, P(3)=0.3

Answer

P(1)=0.5, P(2)=0.3, P(3)=0.2

Answer

P(1)=1, P(2)=0, P(3)=0

Answer

P(1)=0.1, P(2)=0.4, P(3)=0.5

Question 3

What is the key difference between a PMF and a PDF (probability density function)?

Accepted Answer

PMF applies to discrete random variables; PDF applies to continuous random variables

Answer

PMF integrates to 1; PDF sums to 1

Answer

PMF values can exceed 1; PDF values cannot

Answer

PMF and PDF are identical

Question 4

For a valid PMF, can P(X = x₀) = 0 for some specific value x₀ in the support?

Accepted Answer

Yes, a PMF can assign zero probability to values in its defined domain

Answer

No, all defined values must have positive probability

Answer

Only if x₀ is not in the support

Answer

Only if there are infinitely many values

Question 5

What is the support of a PMF?

Accepted Answer

The set of all values x where P(X=x) > 0

Answer

The set of all real numbers

Answer

The range from min to max value

Answer

The set of all values where P(X=x) = 1

Question 6

If P(X = 2) = 0.3, what is P(X ≠ 2)?

Accepted Answer

0.7

Answer

0.3

Answer

1.3

Answer

0