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# How to Draw Samples From the Conditional Distribution?

TopWe all must be aware of calculating Probability of any event. It is defined as possibility of occurrence for any event given a Sample Space. When we talk about concept of conditional distribution of an arbitrary variable, we actually Mean distribution based on joint concept of distribution of an arbitrary variable and concept of Conditional Probability. Let us learn how to draw samples from the conditional distribution.

When conditional probability supposes more than one variable, by limiting the values of all except for one variable to certain values will let us know the distribution of other variables. This is what we call as conditional distribution of values.
Suppose there are two arbitrary variables A and B in conditional distribution such that 4 is one probable value of A, then conditional probability can be stated as follows: Find the probability of some value of 'B' given the value of 'A' as 4. This can also be represented as follows: B | (A = 4).

As conditional distribution is based on the concept of Probability Distribution, like other distributions we can find out the terms related to probability like mean, variance, standard deviation etc. For instance, mean for condition distribution given as B | (A = a) is represented by E (B | (A = x).

In case where values of just specific number of variables are limited to particular values or ranges, a joint conditional distribution of left over variables is obtained. For example, suppose we have 4 arbitrary variables A, B, C and D, then limiting A and B to particular values 'a' and 'b' (respectively) will give us conditional joint distribution of C and D given A = a and B = b.