Normal Distributions

Normal Distributions

Normal distribution is also known as Gaussian distribution. It is one of the most commonly found probability distribution when studying theory of probability; more specifically when studying continuous probability distribution. Normal distribution function is a function in which the output is the probability of the occurrence of an event is such that it lies between two real numbered values. This can be illustrated with the help of the following example.

Consider a group of students that have taken a test. The distribution of marks of the students would be a normal distribution. The corresponding probability distribution of the probability of marks obtained by a particular student would also be normally distributed.

This type of distribution (abbreviated as dist’n) is very important in statistics. When the variable in question is real valued as well as random, then this type of dist’n is used when otherwise the dist’n is now known. It finds application in the fields of social sciences and natural sciences.

It is because of the central limit theorem that this dist’n is very useful. According to this theorem, if the conditions influencing the random variable are mild then the probability distribution is normally distributed around the mean. Even of the original dist’n is not normal, it would still give us a dist’n that is centered around the mean. In general the curve of a normal distribution would look as follows:



As we can see in the above picture, the shape of the curve resembles that of a bell. Therefore a normal dist’n curve is sometimes also called a bell curve. However this is not the only dist’n that is bell shaped, there are others as well, such as: Cauchy’s, Student’s, logistic etc. The normal dist’n function can be given by the following formula:
f(x,μ,σ)=1/(σ√2π)*e^(-(x-μ)^2/(2σ^2 ))

Where,
μ is the mean of the dist’n. It is also sometimes called the expected value of the dist’n. It can also be the median or the mode of the data set.
σ is the standard deviation of the data set. That makes σ^2 the variance of the distribution.

A random variable that follows this type of Gaussian distribution is said to be normally distributed. It is also sometimes called a normal deviate. In this dist’n if we have μ=0 and σ=1, then the dist’n is called a standard normal dist’n or a unit normal dist’n and the random variable which follows this dist’n is said to be standard normal deviate.

The value of a normal dist’n is practically zero when the x value goes beyond 3 standard deviations on either side of the mean. That is why this dist’n becomes useless when there are many outliers in the data set.

The most simple case of a normal dist’n that is called the standard normal dist’n can be defined by the probability density function as follows:
φ(x)= 1/√2π e^(-1/2 x^2 )

The total area under this curve is said to be 1.

Math Phobia

Math phobia is a very common thing in children and parents. As a parent, do you like math. When you were in school, did you fail math was hard, or boring. Sometimes math just looks too difficult. If you let that mental attitudes fester, then you might end up with a phobia. At that time you should take steps to remove the dread of math, but what if your child tells you the same thing in different words – that they have a math phobia.

For Example : Find the value of (1000π)^(2/3)*(512π)^(4/3)
 
Solution : This problem looks hard for some student 
But if you observe
=>1000=2^3*5^3
=>512=2^9
=>(1000π)^(2/3)*(512π)^(4/3)
=>(2^3*5^3π)^(2/3)*(2^9)^(4/3) 
=>(2^3)^(2/3)*(5^3)^(2/3)*π^(2/3)*(2^9)^(4/3)*(π)^(4/3)
=>(2^2)*5^2*2^12*π^(2/3)*π^(4/3)
=>2^(14)*5^2*(π)^[(2/3)+(4/3)]
=>409600π^2                      

Math phobia is the one which is shown by many students, math phobia is the illogical, intense fear of not succeeding in math. It is well known that one is unable to handle the difficulty associated with learning math. Many people assume that math phobia and an inability to be successful in mathematics are inherited from one's parents. Several legitimate factors contribute to, and increase the severity of, this internal representation.

The Teacher

Math tutors play the most important role to remove the dread of math , we know the fact that many students experience math phobia in the traditional classroom, teachers should design classrooms that will make student  feel more successful. The teacher should prepare students in such a manner so that they must have the  level of success or a level of failure which they can tolerate. Therefore, incorrect responses from math tutor must be handled in a positive way to encourage student.

The student can take help of an online math tutor as well. The math tutor needs to stay eager whatever the student’s viewpoint. Like small children like numbers and games with math so they can like math if help throw online math tutor. The methods which are used by the math tutor may affect whether a student feels successful and develops mathematical self-confidence. Finally, parents and teacher attitudes can positively or negatively influence students attitudes toward mathematics, which in turn affect their levels of confidence and this method may useful to remove the dread of math phobia.

Summary:

Math  phobia is common in almost every student. Parents and teacher's right step at the right time can remove this math phobia. Parents should take help from math help online website. Tutor develops student's   mathematical self-confidence.

Educating Through Online

Idea of  Education through Online build on much of the fast development in the field of communication. Practical learning is a relatively new idea in teaching. Online tutoring is an interactive process in which students work in complete coordination with experienced tutors. The interaction between the student and the tutor is one-on-one, live and in real time. All relevant study material is sent via email, and students can engage in live chat with their tutor. For example student has a doubt with a math problem then online math tutor will send step by step solution via  email and via live chat.

Students are taught a mixture of common subjects like English, chemistry or Math .Here math is a subject many students develop a phobia about it and online math tutoring services are ones that are now being in demand. The online Math tutors can do away with the math phobia of many students.

This will because of the learning process for the student. Some of the math tutor will use the animation videos and graphics. The online Math Tutors often use whiteboards. Which gives the tutor and the student a shared screen space. In other words, it serves the purpose of a conventional blackboard that is normally used in a traditional classroom. Math helper try to understand the problems given by each student one-on-one and develop a teaching program as per their convenience.

For example if the student is in grade 3 then math tutor will develop the program as per their understanding label.

Example Which is the same as 10–3
a)4-3
b)4+3                                
c)4/3
d)4*3

Advantages of online tutoring is 24/7  availability and learning at your speed. Online tutoring sessions are customized to match the needs of each individual student. Tutor refer student friendly training methodology that makes the most difficult problems seem like an easy problem for the students.

The dedicated online math tutor can help any student who is weak in maths. With the expert guidance of the tutors a student can attempt any professional exam .The best part about online tutoring is that it operates across all over the continents and students from all over the globe.

Summary : Online tutoring is use full for all grade students and parents, tutors are available 24/7.Education through online is convenient for students, being at home student can clarify their doubts. The online Math tutors can do away with the math phobia of many students.

Online Math Tutoring

In modern life internet is one of the most powerful and far-reaching communication tool and more over online math tutor is one of the most powerful tools. Math Online is a high quality, independent online math tutoring program. For some children, math will be the most difficult thing,When a teacher imparts math knowledge to a student over the Internet, the process is known as online math tutoring.

Now a day free online math tutor is available,these math tutors will teach you maths problem step by step 

For Example Solve 2x^2+7x+6

Here we can write 7x as 4x+3x

=>2x^2+4x+3x+6

Take 2x common

And 3 common 

=>2x(x+2)+3(x+2)

Here (x+2) is common

=>(x+2)(2x+3)

=>x=-2

Or x=-3/2

Math tutor helps parents and children, some are interactive math games, some are tips and videos for studying, some online tutoring, and some others are to help parents learn to teach their kids math concepts and become children math helper.

Online math tutor, you get 24/7 availability of classrooms with highly qualified instructors. You do not need to step out of your house for math tutor and can study at a time of your own choice, with the help of  math tutors you can even schedule your class according to your convenience and interact with the subject matter maths expert as and when required. 

With the help of free online math tutor you can clarify your doubt at any time and any where.

Parallelogram Properties

Properties of a parallelogram

A quadrilateral is a plane geometric figure that has four sides and four vertices. If in such a quadrilateral, both the pairs of the two opposite sides are parallel and they are also congruent to each other, then such a quadrilateral is called a parallelogram. (Abbreviated as ||gm). The figure below shows a sample parallelogram.



In the above picture, ABCD is a parallelogram. The two sides AB and DC are parallel to each other. This is indicated by the single arrows. The other two sides AD and BC are also parallel to each other. This is indicated by double arrows on both the sides. Also the length of the side AB is same as that of DC and the length of the side AD is same as that of BC. The four angles of the parallelogram are: Properties of parallelogram:

1. The first property we already stated in the definition of the parallelogram, that the opposite sides are parallel to each other.

2. The opposite sides are also congruent to each other. This we saw in the figure above and its description.

3. The opposite angles are congruent. Thus in the above figure,
4. The adjacent angles are supplementary. Thus in the above figure:
mmmm
5. The diagonal of a || gm divide the || gm into two congruent triangles. This can be shown with the help of the following figure:

In the above figure, ABCD is a || gm. AC is its diagonal. Now if we consider the triangles DAC and BAC, we see that one of the sides AC is common to both the triangles. We already established as the property number 2 of the || gm that the opposite sides are congruent. Therefore the side DC is congruent to AB and DA is congruent to CB. Therefore by the SSS congruency theorem, the two triangles DAC and BAC are congruent. Hence the property 5 of the || gm stands proved.

6. Area of a parallelogram: Since we just established that the diagonal of the parallelogram divides the || gm into two congruent triangles, if we know the area of one of these triangles we can find the area of the || gm by doubling the area of the triangle. Let us now see how to find the area of the || gm.

Consider the || gm ABCD shown in the figure below:

The triangle BDC has the length of base = DC = b and the altitude = h. The area of this triangle is therefore given by the formula:
∆ =(1/2)*base*height
∆ =(1/2)* b*h

Now we already established that the area of the || gm is twice the area of this triangle. Thus  the area of the | | gm ABCD would be:
A=2* ∆
A=2*(1/2)* b*  h
A=b*h

 Properties of normal distribution is a topic of statistics and therefore shall be tackled under a separate article.