Answer:
As shown in picture, the area is divided into 4 parts: 3 triangles and 1 rectangles.
Total area:
A = smallest triangle + medium triangle + largest triangle + rectangle
= 2 x 2 x 1/2 + 2 x 6 x 1/2 + 4 x (2 + 2 + 6) x 1/2 + 2 x 2
= 2 + 6 + 20 + 4
= 32
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a) 
because it is equal to the area of the shaded region between X=4 and X=6, and the probability that X falls within some interval is given by the area under the PDF.
b) 
because the shaded region is a rectangle of height 1/5 (by virtue of X following a uniform distribution over the interval [2, 7], which has length 5).
Y= 13 over 10x + 2 is the answer. The most important thing to remember when finding the slope of the line is RISE over RUN. When you rise, you go up or down. When you run, you go right or left. Think of RISE over RUN as a fraction.
You find two points on the line and you count up/down a certain amount of spaces, and right/left a certain amount of spaces to go from one point to the other point.
In this equation, we could use the point on the y-axis and the last point we see on the graph located at (10,15). You count up/down vertically first until you reach the horizontal line that the point is on. Then, you count the amount of spaces horizontally it takes you to reach the point. In this problem, you move up 13 spaces, and move to the right 10 spaces. This as a fraction will be 13 over 10, because we rose 13 spaces and we ran 10 spaces to get to our second point. The y-intercept will be the only number that is on the y-axis, which is 2.
Answer:
B
Step-by-step explanation:
see attachment
