In Example 1 we computed the marginal probability density function
The conditional probability density function of Y given X = 1.2 is
The probability that the hole diameter is less than or equal to 4.8 mm given that the thickness is 1.2 mm is P(Y ≤ 4.8 | X = 1.2 ). This is found by integrating
f_(Y|X) (y│1.2) over the region y ≤ 4.8: