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Questions and Answers
What is the function pX in the context of a discrete random vector X?
What is the function pX in the context of a discrete random vector X?
- The expectation of X
- The joint probability density function of X
- The cumulative distribution function of X
- The probability mass function of X (correct)
Which definition of probability does P2 satisfy?
Which definition of probability does P2 satisfy?
- Frequentist definition
- Laplace definition
- Kolmogorov axiomatic definition (correct)
- None of the above
What is the notation P(X = x) equivalent to in the context of a discrete random vector X?
What is the notation P(X = x) equivalent to in the context of a discrete random vector X?
- PX(x)
- FX(x)
- pX(x) (correct)
- fX(x)
What is the condition for a function fX to be a joint probability density function of a continuous random vector X?
What is the condition for a function fX to be a joint probability density function of a continuous random vector X?
What is the probability of the outcome {H} in P2?
What is the probability of the outcome {H} in P2?
What is the relationship between the joint probability density function fX and the cumulative distribution function FX of a continuous random vector X?
What is the relationship between the joint probability density function fX and the cumulative distribution function FX of a continuous random vector X?
What is the probability of the empty set in P2?
What is the probability of the empty set in P2?
How is the probability of a subset A with more than one element defined in Example 1.5?
How is the probability of a subset A with more than one element defined in Example 1.5?
What is the property of the joint probability density function fX of a continuous random vector X?
What is the property of the joint probability density function fX of a continuous random vector X?
What is the joint probability density function of a uniform random vector X ∼ U([0, 1] × [0, 2])?
What is the joint probability density function of a uniform random vector X ∼ U([0, 1] × [0, 2])?
What is the probability of the outcome {0} in Example 1.5?
What is the probability of the outcome {0} in Example 1.5?
What is the purpose of the definition of probability in Example 1.5?
What is the purpose of the definition of probability in Example 1.5?
What is the value of P1X ((0, 1])?
What is the value of P1X ((0, 1])?
What is the cumulative distribution function of a random variable X?
What is the cumulative distribution function of a random variable X?
What is the induced probability of a random variable X1?
What is the induced probability of a random variable X1?
What is the main distinction in types of random variables?
What is the main distinction in types of random variables?
What is the purpose of specifying a probability model?
What is the purpose of specifying a probability model?
What does PX ((−∞, x]) denote?
What does PX ((−∞, x]) denote?
