Consider the triangle with vertices (0, 0), (1, 0), (0, 1). Suppose that (X, Y ) is a uniformly chosen random point from this tr
iangle. (a) Find the marginal density functions of X and Y . (b) Calculate the expectations E[X] and E[Y ]. (c) Calculate the expectation E[XY ].
1 answer:
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Answer:
b.12
Step-by-step explanation:
<u>Key skills needed: Interior Angle Measure Theorem, Equation Creation</u>
1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures
The theorem is:
S is the sum of all interior angle measures
n is the number of sides of the polygon
2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:
--->
---> (7-2) is 5 since 7 - 2 = 5 so -->
---> 5(180) is the same as 5 x 180 which is 900 so -->
This means that the sum of all interior angles is 900 degrees.
3) Now, we have to find out the sum of all the angles that they gave us so:
--->
The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.
4) We have to combine all like terms on the left side:
--->
--->
5) This means that --->
Subtract 288 from both sides and get:
---> (900-288 = 612)
Then divide by 51 from both sides and get:
---> (612 ÷ 51 = 12)
Therefore b.12 is your answer.
<em>Hope you understood and have a nice day!! :D</em>