Applied Mathematics for Electrical Engineering (3130908)

Question-3c ( ii )-OR

BE | Semester-3 Winter-2019 | 26-11-2019

Q3) (c ( ii ))

The marginal probability density function of X is

F_{x} (x) = \int_{0}^{2} f (x, y) d y

F_{x} (x) = \int_{0}^{2} k (x + 2 y) d y

F_{x} (x) = k {(xy + \frac{2 y^{2}}{2})}_{0}^{2}

F_{x} (x) = k [(2 x + 4) - 0]

F_{x} (x) = k (2 x + 4); 0 < x < 1 .

The marginal probability density function of Y is

F_{Y} (y) = \int_{0}^{1} f (x, y) d x

F_{x} (x) = \int_{0}^{1} k (x + 2 y) d x

F_{x} (x) = k {(\frac{x^{2}}{2} + 2 xy)}_{0}^{1}

F_{x} (x) = k [(\frac{{(1)}^{2}}{2} + 2 y (1)) - 0]

F_{x} (x) = k (\frac{1}{2} + 2 y); 0 < y < 2 .