Question

True/False

Type T (for True) or F (for False) for each statement for both Discrete and Continuous random variables.

Question 19

The cdf F(x) is strictly increasing.

Discrete:

Continuous:

Question 20

The cdf F(x) is between 0 and 1 (inclusive).

Discrete:

Continuous:

Question 21

The limit as x → ∞ of F(x) is 1.

Discrete:

Continuous:

Question 22

If x₁ is the largest value in the range of X, then F(x₁) = f(x₁).

Discrete:

Continuous:

Question 23

The pf/pdf f(x) is differentiable everywhere.

Discrete:

Continuous:

Answer 1

Question 19

The cdf F(x) is strictly increasing.

Discrete: TRUE

Continuous: TRUE

F(X) is always increasing

Question 20

The cdf F(x) is between 0 and 1 (inclusive).

Discrete: TRUE

Continuous: TRUE

Since the probability ranges between 0 to 1

Question 21

The limit as x → ∞ of F(x) is 1.

Discrete: TRUE

Continuous: TRUE

As end point of F(X) = 1

Question 22

If x₁ is the largest value in the range of X, then F(x₁) = f(x₁).

Discrete: FALSE

Continuous: FALSE

F(x₁) = f(X< x₁).

Question 23

The pf/pdf f(x) is differentiable everywhere.

Discrete: FALSE

Continuous: TRUE

Differentiability holds for continuous variables only