1. Probability Foundations

Modes Of Convergence — Quiz

Test your understanding of modes of convergence with 5 practice questions.

Practice Questions

Question 1

Which mode of convergence is defined by the convergence of the cumulative distribution functions (CDFs) at all continuity points of the limiting CDF?

Question 2

If a sequence of random variables $\left\{X_n\right\}_{n=1}^{\infty}$ converges to $X$ in probability, what can be said about the convergence of their characteristic functions?

Question 3

Consider a sequence of random variables $\left\{X_n\right\}_{n=1}^{\infty}$ and a random variable $X$. If for every $\epsilon > 0$, $\mathbb{P}(|X_n - X| > \epsilon) \to 0$ as $n \to \infty$, this condition is directly associated with which theorem?

Question 4

Which of the following statements is true regarding the relationship between convergence in $\text{Lp}$ and almost sure convergence?

Question 5

In the context of financial modeling, if a sequence of asset prices converges almost surely, what is a practical implication?