What is the Probability of Y being Greater than 5 Given X Equals a Constant?

In summary, random variable conditioning is a statistical method used to update the probability of an event occurring based on new information or observations. Its purpose is to incorporate new information into the probability distribution of a random variable, resulting in a more accurate estimation of the likelihood of an event occurring. It differs from regular conditioning in that it adjusts the probability of a random variable rather than a single event, allowing for a more comprehensive and flexible approach. Common applications include finance, economics, and engineering, as well as machine learning and artificial intelligence. However, potential limitations include the assumption of independence and the need for large amounts of data.
  • #1
sneaky666
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Homework Statement



Let X and Y be jointly absolutely continuous Random Variables. Suppose X~Exponential(2) and that P(Y>5|X=x)=e-3x. Compute p(Y>5).

Homework Equations



X~Exponential(2) means that its a exponential distribution integrated from -inf to inf, then sub lambda as 2.

The Attempt at a Solution

the answer is 2/5 which is given but i don't get that... here is my prof's solution somehow he got 2/5
http://i.imgur.com/PCgDI.jpg

I don't understand how to get it, i end up getting infinity in the last step
 
Last edited:
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  • #2
nvm i figured it out
 

FAQ: What is the Probability of Y being Greater than 5 Given X Equals a Constant?

What is random variable conditioning?

Random variable conditioning is a statistical method used to update the probability of an event occurring based on new information or observations. It involves adjusting the probability distribution of a random variable based on a known condition or constraint.

What is the purpose of random variable conditioning?

The purpose of random variable conditioning is to incorporate new information into the probability distribution of a random variable, resulting in a more accurate and updated estimation of the likelihood of an event occurring.

How is random variable conditioning different from regular conditioning?

Random variable conditioning differs from regular conditioning in that it involves adjusting the probability of a random variable rather than a single event or outcome. This allows for a more comprehensive and flexible approach to updating probabilities based on new information.

What are some common applications of random variable conditioning?

Random variable conditioning is commonly used in fields such as finance, economics, and engineering to make predictions and decisions based on uncertain or changing conditions. It is also widely used in machine learning and artificial intelligence algorithms.

What are some potential limitations of random variable conditioning?

One potential limitation of random variable conditioning is the assumption that the random variable is independent of the condition being applied. In reality, many variables may be correlated or dependent on each other, which can affect the accuracy of the conditioning. Additionally, random variable conditioning can be computationally expensive and may require large amounts of data to produce accurate results.

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