IB Maths SL Normal Distribution

IB Mathematics SL Normal Distribution
Answers:

1. random variable X normally distributed with mean 25.
The shaded region between 25 and 27 represents 30% of the distribution.
a). Find P(X>27)
Answer:


b). Find the standard deviation of X
Answer:
Let the random variable X , so that



We know that

Since we don’t know the standard deviation of X, we cannot use the inverse normal. Therefore we have to transform the random variable to that of

, using the transformation

we have the following





Using GDC Casio fx-9860G SD
MAIN MENU > STAT>DIST(F5)>NORM(F1)>InvN>

Setting Tail: right
Area: 0.2
:1
:0

We find that the standardized value is 0.8416

Therefore



2. A random variable X is distributed normally with a mean of 20 and variance 9.
a). Find P(X<(or equal to)24.5)
Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:24.5, , and you get


b). Let P(X<(or equal to)k)=0.85
ii). Find the value of k.
Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.85, , and you get

Question and Answer can be found here

http://www.ibmaths4u.com/viewtopic.php?f=11&t=372

IB Maths Revision Notes HL, SL Studies

IB Maths Revision Notes - IB Mathematics HL, SL, Studies Revision Notes by www.IBmaths4u.com


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Non-Smooth Geometry

Month: April 2013

Date: April 29--May 3

Name: Non-Smooth Geometry

Location: Institute for Pure and Applied Mathematics (IPAM), UCLA, Los Angeles, California.

Description

Many contemporary investigations in geometry lead to analytic questions on non-smooth and fractal spaces different from the usual Euclidean setting. In this workshop we intend to pursue some of these directions with an emphasis on more geometric aspects (another workshop in this program on "Analysis on Metric Spaces" has a more analytic bias). Topics will include analytic problems that arise in geometric group theory or for expanding dynamical systems, differentiability properties of Lipschitz functions, currents and isoperimetric problems on metric spaces, quasiconformal geometry of fractals, and sub-Riemannian geometry.

Information

http://www.ipam.ucla.edu/programs/iagws3/.

IB Mathematics SL – Calculus, Application of Differentiation, Kinematics

The question is :

IB Mathematics SL – Calculus, Application of Differentiation, Kinematics

Can someone explain me the basic concepts of Kinematics.

and the answer is at www.ibmaths4u.com

http://www.ibmaths4u.com/viewtopic.php?f=11&t=262

IB Maths SL– Calculus, Application of Differentiation, Kinematics

Velocity (v) measures the rate of change of displacement (s)

i.e.


Acceleration (a) measures the rate of change of velocity (v)

i.e.

When the motion of a particle happens onto the x-axis we have the following basic rules:

If the displacement (s) is positive then the particle is to the right of the origin.
If the displacement (s) is negative then the particle is to the left of the origin.
If the displacement (s) equals zero then the particle is located at the origin.


If the velocity (v) is positive then the particle is moving to the right.
If the velocity (v) is negative then the particle is moving to the left.
If the velocity (v) equals zero then the particle is at rest.


If the acceleration (a) is positive then the velocity of the particle is increasing.
If the acceleration (a) is negative then the velocity of the particle is decreasing.
If the acceleration (a) equals zero then the velocity function has a stationary point.

A very important thing about kinematics is that when both velocity and acceleration are positive or negative, then the speed of the particle is increasing.
If both the velocity and acceleration have opposite signs, then the speed of the particle is decreasing.

IB Maths HL - Normal Distribution

How can we find the mean
of the weight of a population of students which is found to be normally distributed with standard deviation 2 Kg and the 30% of the students weigh at least 53 Kg.

The answer is from www.ibmaths4u.com

Let the random variable W denote the weight of the students, so that



We know that

Since we don’t know the mean, we cannot use the inverse normal. Therefore we have to transform the random variable to that of

, using the transformation

we have the following





Using GDC Casio fx-9860G SD
MAIN MENU > STAT>DIST(F5)>NORM(F1)>InvN>

Setting Tail: right
Area: 0.1
:1
:0

We find that the standardized value is 0.5244

Therefore

On line Integrator

IB Maths On line Integrator from wolfram.com

http://integrals.wolfram.com/index.jsp

Group Theory

A group  is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property. The operation with respect to which a group is defined is often called the "group operation," and a set is said to be a group "under" this operation. Elements , , , ... with binary operation between  and  denoted  form a group if

1. Closure: If  and  are two elements in , then the product  is also in .

2. Associativity: The defined multiplication is associative, i.e., for all , .

3. Identity: There is an identity element  (a.k.a. 1, , or ) such that  for every element .

4. Inverse: There must be an inverse (a.k.a. reciprocal) of each element. Therefore, for each element  of , the set contains an element  such that .

A group is a monoid each of whose elements is invertible.

A group must contain at least one element, with the unique (up to isomorphism) single-element group known as the trivial group.

The study of groups is known as group theory. If there are a finite number of elements, the group is called a finite group and the number of elements is called thegroup order of the group. A subset of a group that is closed under the group operation and the inverse operation is called a subgroup. Subgroups are also groups, and many commonly encountered groups are in fact special subgroups of some more general larger group.

A basic example of a finite group is the symmetric group , which is the group of permutations (or "under permutation") of  objects. The simplest infinite group is the set of integers under usual addition. For continuous groups, one can consider the real numbers or the set of  invertible matrices. These last two are examples of Lie groups.

http://mathworld.wolfram.com/Group.html