Question

Conditional Distribution, Marginal Distribution, Joint Distribution.
What’s the difference?

Answer 1

The concepts of conditional distribution, marginal distribution, and joint distribution are used in statistics to analyze relationships between two variables. The joint distribution represents frequencies or probabilities of different combinations of values, the marginal distribution focuses on each variable individually, and the conditional distribution focuses on subsets of the population based on a specific condition or value.

Step-by-step explanation:

The conditional distribution, marginal distribution, and joint distribution are concepts used in statistics to analyze relationships between two variables in a dataset.

The joint distribution represents the frequencies or probabilities of different combinations of values for the two variables. It is typically presented in a two-way frequency table or as a joint probability function.

The marginal distribution focuses on the frequencies or probabilities of each variable individually, disregarding the other variable. It represents the disconditional distribution focuses on subsets of the population defined by a specific condition or value of one variable. It represents the tribution of one variable while ignoring the other.

The distribution of one variable within a specific condition or value of the other variable.

For example, in a two-way table with gender and favorite sport, the joint distribution represents the frequencies of males and females who prefer different sports. The marginal distribution represents the frequencies of males and females overall, ignoring their sport preferences. The conditional distribution represents the frequencies of different sports within each gender.

Answer 2

Step-by-step explanation:

Marginal distribution: This distribution gives the probability for each possible value of the Random variable ignoring other random variables. Basically, the values of other variables is not considered in the marginal distribution, they can be any value possible. For example, if you have two variables X and Y, the probability of X being equal to a value, lets say, 4, contemplates every possible scenario where X is equal to 4, independently of the value Y has taken. If you want the probability of a dice being a multiple of 3, you are interested that the dice is either 3 or 6, but you dont care if the dice is even or odd.

Conditional distribution: This distribution contrasts from the previous one in the sense that we are restricting the universe of events to specific condition for other variable, making a modification of our marginal results. If we know that throwing a dice will give us a result higher than 2, then to in order to calculate the probability of the dice being a multiple of 3 using that condition, we have two favourable cases (3 and 6) from 4 total possible results (3,4,5 and 6) discarding the impossible values (1 and 2) from this universe since they dont match the condition given (note that the restrictions given can also reduce the total of favourable cases).

The joint distribution calculates the probabilities for two different events (related to two different random variables) occuring simultaneously. If we want to calculate the joint probability of a dice being multiple of 3 and greater than 2 at the same time, our possible cases in this case are 3 and 6 from 6 possible results. We are not discarding 1 or 2 as possible results because we are not assuming, that the dice is greater than 2, that is another condition that we should met in the combination of events.