Marginal Probability of X & Y: Find f(x,y)=cxy

• kuahji
In summary, the marginal probability function for X is f(x) = x/6 for x=1,2,3. This was obtained by summing over y in the joint probability function f(x,y) = cxy and solving for c, which was found to be 1/36. The book confirmed this solution. However, there was some initial confusion as the book had a similar example with a different answer, but it was determined that the book is correct and the solution is f(x) = x/6.
kuahji
Find the marginal probability functions of a) X and b) Y
f(x,y)=cxy for x=1,2,3 y=1,2,3 (discrete data)

The first thing I did was solve for c, which turned out to be 1/36. The book confirmed this.

Next I setup a table, for x=1 the total would be 6c, x=2 12c, x=3 18c.

So for the marginal probability for X, where x=1 I took 6 (1/36) 1/6, x=2 12(1/36)=1/3, & finally x=3 18(1/36)=1/2

so the marginal probability for X is as follows
f(x)= 1/6 for x=1
1/3 for x=2
1/2 for x=3

However, this is what the book has for an answer
f(x)= x/6 for x=1,2,3

So I'm kinda confused here. The book has a similar example & I did this problem exactly like the example, so where am I going wrong?

kuahji said:
Find the marginal probability functions of a) X and b) Y
f(x,y)=cxy for x=1,2,3 y=1,2,3 (discrete data)

The first thing I did was solve for c, which turned out to be 1/36. The book confirmed this.

Next I setup a table, for x=1 the total would be 6c, x=2 12c, x=3 18c.

So for the marginal probability for X, where x=1 I took 6 (1/36) 1/6, x=2 12(1/36)=1/3, & finally x=3 18(1/36)=1/2

so the marginal probability for X is as follows
f(x)= 1/6 for x=1
1/3 for x=2
1/2 for x=3

However, this is what the book has for an answer
f(x)= x/6 for x=1,2,3

So I'm kinda confused here. The book has a similar example & I did this problem exactly like the example, so where am I going wrong?

The book is correct. You need to sum over y.

$$f_X(x)=\sum_{y=1}^3f_{X,Y}(x,y)=\sum_{y=1}^3\frac{1}{36}xy=\frac{1}{36}x(1+2+3)=\frac{x}{6}$$

Edit: I just noticed that you do have the correct answer. Think about it.

Last edited:
Indeed, you are correct... :)

1. What is the concept of marginal probability?

Marginal probability is a type of probability that focuses on the likelihood of one event occurring, regardless of the other events that may also occur. It involves finding the probability of a single variable or event within a larger set of variables or events.

2. How is the marginal probability of X and Y calculated?

To calculate the marginal probability of X and Y, you first need to find the joint probability of X and Y (f(x,y)). This is done by multiplying the individual probabilities of X and Y. Then, you can use the formula P(X) = ∑P(X,Y) to find the marginal probability of X, and P(Y) = ∑P(X,Y) to find the marginal probability of Y.

3. What does the equation f(x,y)=cxy represent in marginal probability?

The equation f(x,y)=cxy represents the joint probability of X and Y, where c is a constant. This means that the probability of both X and Y occurring together is equal to the product of their individual probabilities, multiplied by the constant c.

4. Can marginal probability be used to find the probability of two independent events?

Yes, marginal probability can be used to find the probability of two independent events, as long as the events are not dependent on each other. This is because the joint probability of two independent events is equal to the product of their individual probabilities, which is the same concept used in calculating marginal probability.

5. How is marginal probability useful in scientific research?

Marginal probability is useful in scientific research as it allows for the calculation of the probability of a single variable or event within a larger set of variables or events. This can help in identifying patterns and relationships between variables, as well as making predictions and decisions based on the likelihood of certain events occurring.

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