Question

True/False

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

1. X cannot map two sample points to the same number.

• Discrete:

• Continuous:

2. The sample space (domain) must be discrete.

• Discrete:

• Continuous:

3. The range of X is uncountably infinite.

• Discrete:
  • Continuous:

4. The cdf F(x) is differentiable everywhere.

• Discrete:

• Continuous:

5. The limit as x → ∞ of F(x) is 1.

• Discrete:

• Continuous:

6. The cdf F(x) is right-continuous.

• Discrete:

• Continuous:

7. The pf/pdf f(x) is non-decreasing.

• Discrete:

• Continuous:

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

• Discrete:

• Continuous:

9. E[X²] = Var(X) + (E[X])².

• Discrete:

• Continuous:

10. Variables need to be independent for the CLT to apply.

• Discrete:

• Continuous:

Answer 1