Finding marginal Probability Functions ? Anyone

In summary, a marginal probability function is a function that gives the probability of a single event occurring within a larger set of events. It differs from a joint probability function, which represents the probability of multiple events occurring together. To calculate a marginal probability function, the joint probability function must be summed or integrated over all possible values of the other variables. Finding marginal probability functions is important for analyzing individual events and understanding the relationship between variables. Additionally, a marginal probability function can be used to calculate conditional probabilities using a derived formula.
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Mathemag1c1an
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Finding marginal Probability Functions ? Anyone

I have this question which I cannot seem to solve:
The joint probability mass function p(x, y) of two discrete random variables X and Y is given by.
p(x,y) = ([5^x][7^y][e^-5])/x!(y-x)!
x and y are non-negative integers and x <= y
(i) Find the marginal probability mass functions of X and Y.
 
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  • #2
The marginal probability mass functions of X and Y are given by:p(x) = (5^x e^-5)/x!p(y) = (7^y e^-5)/y!
 

What is a marginal probability function?

A marginal probability function is a function that gives the probability of a single event occurring within a larger set of events. It represents the probability distribution of a single variable, ignoring the values of other variables.

How is a marginal probability function different from a joint probability function?

A joint probability function represents the probability of multiple events occurring together. In contrast, a marginal probability function focuses on the probability of a single event occurring, regardless of the values of other variables.

How do you calculate a marginal probability function?

To calculate a marginal probability function, you need to sum or integrate the joint probability function over all possible values of the other variables. This reduces the joint probability distribution to a single variable, giving you the marginal probability function.

Why is it important to find marginal probability functions?

Finding marginal probability functions is important because it allows us to analyze the probability of individual events within a larger set of events. It also helps us understand the relationship between variables and their impact on the overall probability distribution.

Can a marginal probability function be used to calculate conditional probabilities?

Yes, a marginal probability function can be used to calculate conditional probabilities by using the formula P(A|B) = P(A∩B) / P(B), where P(A|B) represents the probability of event A occurring given that event B has occurred. This formula can be derived from the marginal probability function and the joint probability function.

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