For continuous random variables X and Y with joint probability density function

a. Find P(X > 1 and Y > 1).

b. Find the marginal probability density functions fX(x) and fY(y).

c. Are X and Y independent? Explain.

Solution 16E

Step1 of 3:

We have continuous random variables X and Y with joint probability density function

Here our goal is:

a).We need to find P(X > 1 and Y > 1).

b).We need to find the marginal probability density functions

c).We need to check Are X and Y independent? Explain.

Step2 of 3:

a).

Consider,

Integrate above equation with respect to “y” we get

=

= 0 - (-)

=

Where “e” is mathematical constant and its value is approximately 2.71828. Substitute “e” i above equation we get

=

=

=

= 0.0676

Therefore, = 0.0676.

Step3 of 3:

b).

Consider,

1).If Therefore, ) = 0.

2).If Then

=

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