Suppose you have been given two Random Variables X and Y, whose joint distribution is already known, the marginal distribution of X is simply the probability distribution of X averaging over…

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Options

• AThis is typically calculated by summing the joint probability distribution over Y.
• BThis is typically calculated by integrating the joint probability distribution over Y
• CThis is typically calculated by summing (In case of discrete variable) the joint probability distribution
• DThis is typically calculated by integrating(ln case of continuous variable) the joint probability

• A
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Explanation

Given two random variables X and Y whose joint distribution is known, the marginal distribution of X is simply the probability distribution of X averaging over information about Y. It is the probability distribution of X when the value of Y is not known. This is typically calculated by summing or integrating the joint probability distribution over Y. ' For discrete random variables, the marginal probability mass function can be written as Pr(X = x). where Pr(X = x,Y = y) is the joint distribution of X and Y, while Pr(X = x|Y = y) is the conditional distribution of X given Y In this case, the variable Y has been marginalized out. Bivariate marginal and joint probabilities for discrete random variables are often displayed as two- way tables. Similarly for continuous random variables, the marginal probability density function can be written as pX(x). This is where pX.Y(x.y) gives the joint distribution of X and Y while pX|Y(x|y) gives the conditional distribution for X given Y Again: the variable Y has been marginalized out. Note that a marginal probability can always be written as an expected value: Intuitively, the marginal probability of X is computed by examining the conditional probability of X given a particular value of Y, and then averaging this conditional probability over the distribution of all values of Y This follows from the definition of expected value, i.e. in general

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