Simple joint probability distribution

In summary, the conversation covers the joint probability distribution between two machines, X and Y, where Y is connected to X and is dependent on its turning on. It is stated that X turning on leads to a 50% chance of Y turning on and if Y does turn on, there is a 25% chance of it breaking. The conversation also mentions that Y cannot turn on spontaneously and can only be turned on through X. The question asks for the joint probability distribution between Y turning on and Y breaking, as well as the mutual information between the two events.
  • #1
jetlam
3
0

Homework Statement



Let's say there are two machines, X and Y. X is connected to Y.

* If X is turned on, Y turns on 50% of the time.
* If Y turns on (through X being turned on) then it breaks 25% of the time.
* Y won't break spontaneously and it can only be turned on through X.

What is the joint probability distribution between Y turning on and Y breaking?
Considering the set of times that X turns on, what is the mutual information between Y turning on and Y breaking (how many bits)?

Thanks.

2. The attempt at a solution

I'm not really sure how to start or how to make the joint probability distribution.
 
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  • #3

What is a simple joint probability distribution?

A simple joint probability distribution refers to the probability distribution of two or more random variables that are mutually dependent. It shows the likelihood of different combinations of values occurring for these variables.

How is a simple joint probability distribution different from a marginal distribution?

A marginal distribution shows the probability distribution of a single random variable without considering other variables. In contrast, a simple joint probability distribution takes into account the relationship between multiple variables and provides a more comprehensive view of their probabilities.

What is the formula for calculating the probability of a specific combination of values in a simple joint probability distribution?

The formula for calculating the probability of a specific combination of values (x, y) in a simple joint probability distribution is P(X = x and Y = y) = P(X = x) * P(Y = y|X = x), where P(X = x) is the marginal probability of X = x and P(Y = y|X = x) is the conditional probability of Y = y given X = x.

What is the difference between a joint probability and a conditional probability?

A joint probability refers to the probability of two or more events occurring simultaneously, while a conditional probability refers to the probability of one event occurring given that another event has already occurred. In a simple joint probability distribution, the conditional probability is used to calculate the probability of a specific combination of values for two variables.

What are some real-world applications of a simple joint probability distribution?

A simple joint probability distribution can be used in various fields such as finance, engineering, and medicine. For example, it can be used to model the relationship between risk factors and disease in medical research or to predict stock market returns based on the performance of different variables. It can also be used in quality control to identify the factors that affect the production process and their probability of occurrence.

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