The probability distribution of
Assume
We can determine the conditional probability in terms of discrete random variables if we know the value of
This provides us with the conditional probability mass function of
Suppose
Compute
Let's put the values in the formula mentioned above:
If
Likewise, when
Therefore, for a very small
Because
Let's evaluate the steps above:
The probability density function for
Joint density functions of
Where,
Compute
Using the definition given:
Putting values in
Now we'll calculate the values below:
Two events
If
If
Conditional distributions are helpful when we collect data for two variables, such as gender and income preference. Still, we are interested in solving probability questions when we know the value of one of the variables. In real life, there are numerous cases where we know the value of one variable and may use a conditional distribution to determine the likelihood of another variable taking on the specific value.
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