Which of the following best describes the solution to the system of equations below?
2 answers:
Answer: Option D
Step-by-step explanation:
The equation of the line in slope intercept form is:
Where m is the slope and b the y-intercept.
Solve for y from both equations:
As you can see, the slopes of the lines are equal, therefore, they are parallel.
If the lines are parallel then the system of equtions has no solution.
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(1) Looks like the joint density is
In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is
(2) The region in which <em>X</em> > 2 and <em>Y</em> < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is
(3) Are you supposed to find the marginal density of <em>X</em>, or the conditional density of <em>X</em> given <em>Y</em>?
In the first case, you simply integrate the joint density with respect to <em>y</em>:
In the second case, we instead first find the marginal density of <em>Y</em>:
Then use the marginal density to compute the conditional density of <em>X</em> given <em>Y</em>:
