Choose the correct definition of a sampling distribution. The sampling distribution of a statistic of size isa.the distribution
1 answer:
You might be interested in
break it up into simpler shapes. See the photo.
There is:
trapezoid
A = 0.5(3.2+6.5)4.5
= 21.825
triangle
A = 0.5(2.7)4.5
= 6.075
rectangle
A = 1.8(4.5)
= 8.1
Total Area = 21.825 + 6.075 + 8.1
= 36
There is:
trapezoid
A = 0.5(3.2+6.5)4.5
= 21.825
triangle
A = 0.5(2.7)4.5
= 6.075
rectangle
A = 1.8(4.5)
= 8.1
Total Area = 21.825 + 6.075 + 8.1
= 36
Split up the integration interval into 4 subintervals:
The left and right endpoints of the -th subinterval, respectively, are
for , and the respective midpoints are
- Trapezoidal rule
We approximate the (signed) area under the curve over each subinterval by
so that
- Midpoint rule
We approximate the area for each subinterval by
so that
- Simpson's rule
We first interpolate the integrand over each subinterval by a quadratic polynomial , where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
