Sampling Distributions

Let us study about Sampling Distributions,
Sampling variability is the tendency of the same statistic computed from a number of random samples drawn from the same population to differ.

Suppose that the first sample of 100 magazine subscribers was “returned” to the population (made available to be selected again), another sample of 100 subscribers selected at random, and the mean income of the new sample computed. If this process were repeated ten times, it might yield the following sample means:

27,500 27,192 28,736 26,454 28,527

28,407 27,592 27,684 28,827 27,809

These ten values are part of a sampling distribution. The sampling distribution of a statistic—in this case, of a mean—is the distribution obtained by computing the statistic for a large number of samples drawn from the same population.
Hope the above explanation helped you.

Multiplying Polynomials

In this session i will explain how to Multiply Polynomials,

The following are rules regarding the multiplying of variable expressions.

Rule 1: To multiply monomials with the same base, keep the base and add the powers:
Rule 2: To find the power of a base, keep the base and multiply the powers.
Rule 3: To find a power of a product, raise each factor in the product to the power.
I hope the above explanation was useful, now let me explain about remainder theorem.

Law of Sines

Let us study about Law of Sines,
You can use the Law of Cosines discussed in the last section to solve general triangles, but only under certain conditions. The formulas that will be developed in this section provide more flexibility in solving these general triangles.

The following discussion centers around Figure 1 .
Figure 1

Reference triangles for Law of Sines.

Line segment CD is the altitude in each figure. Therefore Δ ACD and Δ BCD are right triangles. Thus,


In Figure 1 (b), ∠CBD has the same measure as the reference angle for β Thus,
It follows that


Similarly, if an altitude is drawn from A,


Combining the preceding two results yields what is known as the Law of Sines.
In other words, in any given triangle, the ratio of the length of a side and the sine of the angle opposite that side is a constant. The Law of Sines is valid for obtuse triangles as well as acute and right triangles, because the value of the sine is positive in both the first and second quadrant—that is, for angles less than 180°. You can use this relationship to solve triangles given the length of a side and the measure of two angles, or given the lengths of two sides and one opposite angle. (Remember that the Law of Cosines is used to solve triangles given other configurations of known sides and angles).

First, consider using the Law of Sines to solve a triangle given two angles and one side.
Hope the above explanation was helpful.

The Midpoint Theorem

Let us understand what is midpoint theorem,

Figure 1 shows Δ ABC with D and E as midpoints of sides AC and AB respectively. If you look at this triangle as though it were a trapezoid with one base of BC and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids, Theorem 55.


Theorem 56 (Midpoint Theorem): The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

In Figure 1 , by Theorem 56,


Hope the above explanation helped you, now let me on properties of trapezoids.