# The difference btwn marginal distribution and conditional distribution ?

• Dani16
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Dani16
The difference btwn marginal distribution and conditional distribution ?

So I have a table that "apparently" shows how a company's employees commute to work.

TRANSPORTATION
JOB CLASS CAR BUS TRAIN TOTAL
MANAGEMENT 26 20 44 90
LABOR 56 106 168 330
TOTAL 82 126 212 420​

As you look at my sorry attempt to re-create the table I was given...
So now I must find the marginal ditrubution (in %) of mode of transportation as well as the conditional distribution (in%) of mode of tranportation for management.

When I read the definition of a conditional distribution in lead me to think that in order to find that I would divide the data under management [26,20,44] by the total [90].

The marginal distribution I am lost on.

Can someone help me ? Please ?
Thank you !

You have to find the individual probability of each mode of transportation
for instance : P(Car)=(82/420)
P(BUS)=(126/420)
p(tRAIN)=212/420
SUM OF PROB EQUAL ONE, SO YOU HAVE A MARGINAL DISTRIBUTION.
FOR THE CONDITIONNAL ONE i THINK YOU ARE RIGHT, YOUR CONDITION IS WELL MANAGEMENT.

You have two marginal distributions: (1) the distribution of transportation mode (i.e., what percentages of ALL employees---both labor and management---take car, bus or train; and (2) the distribution of employee type (i.e., what percentage of employees are labor and what percentage are management).

RGV

## 1. What is the definition of marginal distribution?

Marginal distribution refers to the probability distribution of a subset of a larger set of random variables. It represents the probabilities of all possible outcomes for that subset, without taking into account the other variables in the larger set.

## 2. How is marginal distribution different from conditional distribution?

Marginal distribution considers the probabilities of a subset of variables without considering the other variables, while conditional distribution takes into account the probability of one variable given the value of another variable. In other words, marginal distribution looks at the overall probabilities while conditional distribution looks at the specific probabilities within a subset.

## 3. How are marginal and conditional distributions related?

Marginal and conditional distributions are related through the joint distribution of all the variables. Marginal distribution can be obtained by summing or integrating over the joint distribution for the variables not of interest, while conditional distribution can be obtained by dividing the joint distribution by the marginal distribution of the conditioning variable.

## 4. In what situations are marginal and conditional distributions commonly used?

Marginal distributions are commonly used when looking at the overall probabilities of a subset of variables, such as in market research or polling data. Conditional distributions are commonly used when studying the relationship between two variables, such as in regression analysis or medical studies.

## 5. Can marginal and conditional distributions change over time?

Yes, both marginal and conditional distributions can change over time depending on the variables being studied and the underlying factors influencing them. As new data is collected, the distributions may shift or change, and it is important for scientists to consider these changes when making conclusions or predictions based on the distributions.

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