Expected Value and Conditional Probability

In summary, expected value is the average outcome of a random experiment calculated by multiplying each possible outcome by its probability of occurring and summing them together. It is commonly used in decision-making to compare potential outcomes of different choices. Conditional probability, on the other hand, is the likelihood of an event occurring given that another event has already occurred. It is often used in real-world scenarios such as medical diagnosis and weather forecasting to make more accurate predictions. Although both involve calculating probabilities, expected value focuses on average outcomes while conditional probability considers the influence of other factors on the likelihood of an event occurring.
  • #1
retspool
36
0
So i a need to find E[XY], expected value of XY

But the process of finding E[X] includes a long and tideous integral which i am trying to avoid.
So computing E[XY] using its formula is also something i am trying to avoid.

But could i use this identity?

E[XY] = E[E(XY/Y)] = E[Y[E(X/Y)]]

Since I've already found E[X/Y] = Y, it gives me E[Y.Y] = E[Y^2].

Is the identity true?
 
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  • #2
I deduced the identity from the given forumla

E[X] = E(E[XY/Y])
 

Related to Expected Value and Conditional Probability

1. What is expected value?

Expected value is a concept in probability and statistics that represents the average outcome of a random experiment over a large number of trials. It is calculated by multiplying each possible outcome by its probability of occurring and summing all of these values together.

2. How is expected value used in decision-making?

Expected value is commonly used in decision-making to evaluate the potential outcomes of different choices. By comparing the expected values of each option, one can make a more informed decision about which choice is likely to result in the most favorable outcome.

3. What is conditional probability?

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of the two events by the probability of the given event.

4. How is conditional probability used in real-world scenarios?

Conditional probability is used in a variety of real-world scenarios, such as in medical diagnosis, weather forecasting, and financial risk assessment. It allows us to make more accurate predictions by taking into account the influence of other factors on the likelihood of an event occurring.

5. What is the relationship between expected value and conditional probability?

Expected value and conditional probability are related in that they both involve calculating probabilities of events. However, expected value focuses on the average outcome of a random experiment, while conditional probability considers the likelihood of an event occurring given that another event has already occurred.

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