Question

If f(x,y) is a joint probability density function then the formula to find the marginal density
function of 'X' is
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Answer 1

Answer:

f X , Y ( x , y ) = { 1 π , x 2 + y 2 ≤ 1 , 0 , otherwise . The marginal PDF of X can be found as follows: f X ( x ) = ∫ - ∞ ∞ f X , Y ( x , y ) d y = ∫ - 1 - x 2 1 - x 2 1 π d y = 2 π 1 - x 2 , - 1 ≤ x ≤ 1. ... Clearly, this is not equal to the joint PDF, and therefore, the two random variables are dependent