18 Questions
What is the function pX in the context of a discrete random vector X?
The probability mass function of X
Which definition of probability does P2 satisfy?
Kolmogorov axiomatic definition
What is the notation P(X = x) equivalent to in the context of a discrete random vector X?
pX(x)
What is the condition for a function fX to be a joint probability density function of a continuous random vector X?
fX is non-negative and integrates to 1
What is the probability of the outcome {H} in P2?
p
What is the relationship between the joint probability density function fX and the cumulative distribution function FX of a continuous random vector X?
FX(x) = ∂/∂x1 ... ∂/∂xp fX(x) for almost all x ∈ Rp
What is the probability of the empty set in P2?
0
How is the probability of a subset A with more than one element defined in Example 1.5?
As the sum of probabilities of individual outcomes
What is the property of the joint probability density function fX of a continuous random vector X?
fX is non-negative
What is the joint probability density function of a uniform random vector X ∼ U([0, 1] × [0, 2])?
f(x1, x2) = 1/2, (x1, x2)′ ∈ [0, 1] × [0, 2]
What is the probability of the outcome {0} in Example 1.5?
0.018
What is the purpose of the definition of probability in Example 1.5?
To free the mathematical meaning of probability from the random experiment
What is the value of P1X ((0, 1])?
1/2
What is the cumulative distribution function of a random variable X?
FX (x) = PX ((−∞, x])
What is the induced probability of a random variable X1?
PX1 (B) = P1 (N0 ∩ B) p
What is the main distinction in types of random variables?
Discrete and continuous
What is the purpose of specifying a probability model?
To introduce a shortcut for computing probabilities
What does PX ((−∞, x]) denote?
The probability that X is less than or equal to x
Learn about the probability mass function and joint probability density function of discrete and continuous random vectors, including definitions and notation.
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