Does P(X>t) Differ from P(Y>t) When X>Y>t?

In summary, the question is asking whether P(X>t) is larger or smaller than P(Y>t) given that X>Y>t. The answer is that P(X>t) is greater than or equal to P(Y>t), as X>Y implies X>t and Y>t. However, this may not be the point of the question, as it may be discussing stochastic dominance and two-sample location problems.
  • #1
forumfann
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I am confused on a basic probability inequality, could anyone help me on this:
If X>Y>t, then is P(X>t) larger or smaller than P(Y>t)?

Thanks
 
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  • #2
I am confused about this. You start by asserting that "X> Y> t". Given that, P(x> t) and P(Y> t) are both 1.0!

If you just mean that X and Y are random variables, requiring that X> Y, and t is some number, then, yex, P(X> t) is greater than or equal to P(Y> t) (not necessarily larger- they might be equal). If Y> t, then X> t follows from X> Y. But X> t may be true even if Y> t is not.
 
  • #3
This may not be the point of the question about the r.vs, but: we say that the random variable [tex] Y [/tex] is stochastically larger than the random variable [tex] X [/tex] provided that

[tex]
P(Y > t) \ge P(X > t), \quad \forall t
[/tex]

This idea is one way of discussing two-sample location problems.
 

FAQ: Does P(X>t) Differ from P(Y>t) When X>Y>t?

What is a basic probability inequality?

A basic probability inequality is a mathematical concept that describes the relationship between the probability of an event and its complement. It states that the probability of an event occurring is always less than or equal to 1, and the probability of the event not occurring is always greater than or equal to 0.

How is a basic probability inequality calculated?

A basic probability inequality is calculated using the formula P(A) + P(A') = 1, where P(A) represents the probability of an event occurring and P(A') represents the probability of the event not occurring.

What are some real-world applications of basic probability inequalities?

Basic probability inequalities are used in various fields, such as statistics, economics, and engineering, to calculate the likelihood of an event or outcome. They are also used in risk assessment and decision making processes.

Can a basic probability inequality be violated?

No, a basic probability inequality cannot be violated as it is a fundamental mathematical concept that is always true.

How does a basic probability inequality differ from other probability concepts?

A basic probability inequality is a specific inequality that applies to all probability events, while other probability concepts, such as Bayes' theorem and the law of total probability, are more specific and may only apply to certain types of events or scenarios.

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