Part 3 of 3 This gives us 글|10 cos(0) + 20 cos(금) + 20 cos() + 20 cos( cos() cos()] T4 + 10 8.957589 (rounded to six decimal places) Therefore, using the Trapezoidal Rule with n = 4 and rounding to six decimal places we have 10 cos(x2) dx x 8.25245
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
answer part 3
![Estimate
10 cos(x?) dx using the following rule with n = 4.
Exercise (a)
the Trapezoidal Rule
Part 1 of 3
The Trapezoidal Rule says that
f(x) dx * Tn = X [F(xo) + 2f(x1) + ... + 2f(xn - 1) + f(xp)].
We need to estimate
10 cos(x2) dx with n = 4 subintervals.
We have
Ax = 1/4
0.25
Therefore,
Ax
1/8
0.125
Part 2 of 3
We know that xo represents the beginning of the first subinterval, so xo = 0 V
and x1 is the
endpoint of the first sub-interval (which is also the beginning of the second subinterval), and so
X1 = 1/4
0.25 .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf92d748-d709-48ef-b283-787f4c5053b9%2Ffd961947-f5b6-4cac-9e28-5b94e4edbef2%2Fovrzip_processed.jpeg&w=3840&q=75)
Given the integral is,
The above function is to be calculate by 4 trapezoids as,
Here,
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