Practice Partial Differential Equations (17) - Independence of Random Variables

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6 sample questions

Question 1.
Define a random variable.
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Think about the outcomes of a certain experiment.
Question 2.
What does a Probability Mass Function (PMF) describe?
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What type of variable is countable?
3Question 3.
What is the definition of independent random variables?
- They influence each other's distribution
- They do not affect each other's probabilities
- They must have the same mean
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Think about how one event might not influence another.
4Question 4.
For discrete variables, P(X=x, Y=y) = P(X=x) * P(Y=y) holds true if they are independent. True or False?
- True
- False
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Recall the definition you studied.
Question 5.
Given a joint distribution P(X,Y) = P(X)P(Y) where P(X=1) = 0.5, P(Y=1)=0.4, find P(X=1, Y=1).
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Think about using the independence condition.
Question 6.
Prove that two random variables are dependent if P(X=x,Y=y) does not equal P(X=x)P(Y=y).
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Consider cases where the multiplication law fails.

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