Given that the probability space (S, , P), there S is the amount if outcomes, F is the of events and P is a given probability measure of S. A real value random variable is a function X from S to the real numbers R. Which of the statements follow relevant definitions and axiom. 1. X<0 is an event

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Given that the probability space (S, F, P), there S is the amount if outcomes, F is the family
of events and P is a given probability measure of S. A real value random variable is a
function X from S to the real numbers R.
Which of the statements follow relevant definitions and axiom.
1. X<0 is an event
2. It always applies that P(X < ∞) = 1
3. If defines Y = X so that it is a real value random variable
4. For the variable Y = X? it applies that P(Y > 0)> 0|
Transcribed Image Text:Given that the probability space (S, F, P), there S is the amount if outcomes, F is the family of events and P is a given probability measure of S. A real value random variable is a function X from S to the real numbers R. Which of the statements follow relevant definitions and axiom. 1. X<0 is an event 2. It always applies that P(X < ∞) = 1 3. If defines Y = X so that it is a real value random variable 4. For the variable Y = X? it applies that P(Y > 0)> 0|
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