Answer:
<u>sum</u><u> </u><u>is</u><u> </u><u>1</u><u>2</u><u>7</u><u>5</u>
Step-by-step explanation:
![sum = \frac{n}{2} [2a + (n - 1)d] \\ \\ sum = \frac{50}{2} [(2 \times 1) + (50 - 1) \times 1] \\ \\ sum = 25(51) \\ sum = 1275](https://tex.z-dn.net/?f=sum%20%3D%20%20%5Cfrac%7Bn%7D%7B2%7D%20%5B2a%20%2B%20%28n%20-%201%29d%5D%20%5C%5C%20%20%5C%5C%20sum%20%3D%20%20%5Cfrac%7B50%7D%7B2%7D%20%5B%282%20%5Ctimes%201%29%20%2B%20%2850%20-%201%29%20%5Ctimes%201%5D%20%5C%5C%20%20%5C%5C%20sum%20%3D%2025%2851%29%20%5C%5C%20sum%20%3D%201275)
Answer:
(a) 120 square units (underestimate)
(b) 248 square units
Step-by-step explanation:
<u>(a) left sum</u>
See the attachment for a diagram of the areas being summed (in orange). This is the sum of the first 4 table values for f(x), each multiplied by 2 (the width of the rectangle). Quite clearly, the curve is above the rectangle for the entire interval, so the rectangle area underestimates the area under the curve.
left sum = 2(1 + 5 + 17 + 37) = 2(60) = 120 . . . . square units
<u>(b) right sum</u>
The right sum is the sum of the last 4 table values for f(x), each multiplied by 2 (the width of the rectangle). This sum is ...
right sum = 2(5 +17 + 37 +65) = 2(124) = 248 . . . . square units
From the given density function we find the distribution function,

(a)



(b)



(c)



3+3=6 therefore the answer would be 6x.