Independent random variables : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- What does it mean when we say that two events are independent?
- What does it mean when we say that two random variables are independent?
- If the random variables $X$ and $Y$ are NOT independent is the following equality guaranteed to never hold $P(X=1 \wedge Y=2)=P(X=1)P(Y=2)$? Explain your reasoning.
- Is the probability of getting a 3 when I roll a dice independent of the probability of getting a 2 on the same roll? Explain your reasoning.
- Is the following statement true or false "the set of values which a random variable can take all correspond to events that are independent of each other." Explain your reasoning.
- Given the following equation $P(X=x | Y=a \wedge Z=b)=P(X=x | Y=a)$ what can you conclude about the independence of the random variables $X$, $Y$ and $Z$.
- What does it mean when we say that two events are independent?
- What does it mean when we say that two random variables are independent?
- If the random variables $X$ and $Y$ are NOT independent is the following equality guaranteed to never hold $P(X=1 \wedge Y=2)=P(X=1)P(Y=2)$? Explain your reasoning.
- Is the probability of getting a 3 when I roll a dice independent of the probability of getting a 2 on the same roll? Explain your reasoning.
- Is the following statement true or false "the set of values which a random variable can take all correspond to events that are independent of each other." Explain your reasoning.
- Given the following equation $P(X=x | Y=a \wedge Z=b)=P(X=x | Y=a)$ what can you conclude about the independence of the random variables $X$, $Y$ and $Z$.