What is a Marginal Distribution and How Does it Apply to F1(x)F2(y)?

In summary, the speaker is trying to understand the concept of marginal distribution and how it applies to a one-dimensional cumulative distribution function, I(x,y)=F1(x)F2(y). They mention that if X and Y are independent, then the marginal distributions can be expressed as P(X<=x) and P(Y<=y). They also mention a general expression for marginal distributions using intervals where the random variables are defined. However, they are unsure if their understanding is correct and ask for the definition of a marginal distribution and how it applies to F1(x)F2(y).
  • #1
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I'm not sure I understnad what is a marginal distribution, but i need to show that if F1,F2 are one dimensional cummulative distribution functions then I(x,y)=F1(x)F2(y) has F1 and F2 as its marginal distributions.

well if I(x,y)=P(X<=x,Y<=y) and if X and Y are independent, then it equals: P(X<=x)*P(Y<=y), then F1(x)=P(X<=x) F2(y)=P(Y<=y)
or in general: F1(x)=P(X<=x, Y[tex]\in[/tex]A) F2(y)=P(X [tex]\in[/tex] B Y<=y) where A and B are intervals where the r.vs Y and X are defined.

but it's really a guess.
 
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  • #2
What is the definition of a marginal distribution? How does that def. apply to F1(x)F2(y)?
 

1. What is a marginal distribution?

A marginal distribution in statistics refers to the probability distribution of the values of one or more variables in a subset of a larger dataset. It is obtained by summing or averaging the joint probability distribution over the values of the other variables.

2. How is a marginal distribution different from a joint distribution?

A joint distribution represents the probability of two or more variables occurring together, while a marginal distribution focuses on the probability of one variable occurring regardless of the values of the other variables. In other words, a marginal distribution is a simplification of a joint distribution.

3. What is the purpose of calculating marginal distributions?

The purpose of calculating marginal distributions is to gain a better understanding of the relationship between variables in a dataset. It can also help to identify any patterns or trends in the data and to make predictions about the values of one variable based on the values of others.

4. Can a marginal distribution be used to make inferences about a population?

Yes, a marginal distribution can be used to make inferences about a population, especially if the subset of data used to calculate the marginal distribution is representative of the entire population. However, caution should be taken as a marginal distribution may not accurately represent the true population distribution.

5. How is a marginal distribution represented graphically?

A marginal distribution can be represented graphically using a histogram, bar chart, or line graph. The specific type of graph used will depend on the type of variable being analyzed (e.g. categorical or continuous) and the number of variables involved. It is important to choose a graph that effectively displays the distribution of the data.

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