1 thought on “If f(x,y) is a joint probability density function then the formula to find the marginal density<br />function of ‘X’ is<br />”
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
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