₦airaland Forum

Ayowumie: @echibuzor, yes I have read it up.what I'm batttling with is critiquing an article's report of ANOVA and linear regression. If u cud b of help, I wudnt mind sendin it to ur email pls

Send it... I am not too confident tho... Statistics is not my strong suit...

1a.

of the 25 members of the orchestra, we have a 32 year old lady..

Average age => (x + 32)/25 = y where x is the sum of the ages of the other 24 persons/people (i no hear english) and y is the average

by making x the subj.of the form.. we have x = 25y - 32 ---- i

When the 32 year old is replaced by a 30 year old

Average becomes => (x + 30)/25 = z where z is the new average...
making x the subj. of the form.. we have x = 25z - 30 -----ii

Substitue for x in either equations to give...

25y - 32 = 25z - 30 (collect like terms)

25y - 25z = -30 + 32

25(y - z) = 2

y - z = 2/25 = 0.08

y is the initial average and z is the final average.

It is obvious that the difference in both average is 0.08 Q.E.D

I will give the b part a shot...j

The median will not be affected at all. Because in ascending or descending order, 30 will replace 32 at the extreme end of the sequence without changing the order (30 will be the new youngest.)....

answer to 1a is 0.08... Uploading pictures.is not going through... I ll try typing it.. gimme some minutes...

Noah2020: Pls i nid sum1 to help me wit dis question. An orchestra consists of 25 members. The youngest member is 32 years old. She leaves and is replaced by a new member who is 30 yearsold.
1A : 2.0 points
By how much does the replacement change the average age of the membersof the orchestra? 1B :
By how much does the replacement change the median age of the members of the orchestra?

Are you sure there is no typo in this question....

I am having a go at the first question...
Malthusian Growth model also known as the Exponential Model...

Change in Population is directly proportional to Change in Time..

dP @ dt
dP = k dt
§dP = k§dt
Ln P = kt + c
P = e^[kt + c)
P = e^ (kt) * e^c [let e^c =A)
P = Ae^kt....... [i]
{at t = 0, P = P© [ read P© as P not [peanut]]
P© = Ae^k0
P© = A...
P<t> = P© e^kt........

For the calculation, I got 2109.something...

And here comes another one....
This actually the trick Question...


(a) The population of the world was 5.28 billion in 1990 and 6.07 in 2000. Find an exponential model for these data and use the model to predict the world pop. in the year 2020?

According to the model in part (a), when will the world pop. exceed to 10 billion?

Using the data in part (a) to find a logistic model for the pop. Assume a carrying capacity of 100 billion. Then use the model to predict the pop. in 2020.

According to the logistic model, when will the world pop. exceed 10 billion?

First let someone derive a comprehensive Malthusian Growth model and then we can begin from there...

I havent tried solving this question, saw it on the internet. But, hey! lets see what you got...


The population of a country is 6 million in 2010 and growing at a rate of 1.4% each year. If the rate of population growth remains constant, the population will reach 24 million in...


Its an objective question but I did not include in my CTRL C.....

Chibuzor

If anyone has questions on Modelling and Simulation, Operations Research, Queue Theory, Markov Chain... They should post them. These are some of the areas of mathematics that cuts across several Fields... And of course Calculus.. We all can learn a thing or too.. No man is an island of knowledge.....

Chibuzor...

I have a trick Question coming up... Its on Modeling...

@rottable..... Greatest OOUites.....
Dont mind the guy with the baptismal solution.... What u should ask ursef is What do you want o do? When that is settled, Then you ask if you have the required skills to perfom well in that which you want to do... If you are confident you have them, good.. If not, go ahead and acquire them... Then you cam start to apply for that job.... No Organisation wants to send staff on expensive training anymore.... Thats my 2kobo.... Excellentia Humania est patriae Opus....

Richiez: @chibuzor i'm extremely impressed. 10ks

You are welcome chief... Its my pleasure to be of service....

A field is a ring with inverses and identity for the two operations... (Thats explanatory enuf right?)

Illustrations.....

A Field F = {S,01,02,11,12} where S is the set, 01 is the first operation (lets say addition), the inverse of which is subtraction, 02 is the second operation (lets say Multiplication), the inverse of which is division, 11 is the identity of the first operation (in this case (0) for addition) and 12 is the identity of the second operation (in this case (1) for multiplication)

Bear in mind that it must satisfy all the conditions which are required for a Ring (See my previous post)...
I think that wraps it for now.........



@Ayowumie... Its not possible to discuss/teach ANOVA from the scratch over the internet....... You read up and ask questions...
Thank you...
Chibuzor

A Ring is an algebraic system consisting of a set, an identity element (see my previous post), two operations and the inverse of the first operation...
Example... ring R = {S, 01, 02, 1} where S is the set of Real numbers (You all know what Real Numbers are right?) , 01 is the opeartion of addition, the inverse of which is subtraction, 02 is the operation of multiplication, 1 is the identity element which for for addition (which is the first operation) is zero (0).

Still too abstract right? Lets get practical...

A ring is mostly called Commutative ring because Commutativity (Google) must be met before a Set of elements can be called a RING..

Illustration...

Let R (Real Numbers) be a set on which two binary operations (A binary operation is an opeation that needs exactly two inputs before it can return an output) are defined, Operations are Addition +, and Multiplication *.

Then R is a Commutative Ring if the following axioms hold...
(1) Closure - If a,b R, (Please ask quetion if you dont undastand notations) then the sum a+b and the product a*b are uniquely defined (returns an output) and belong to the set R (Closure)

(2) Associative Laws (Associativity) - For all a,b,c R, a+(b+c) = (a+b)+c and a*(b*c) = (a*b)*c. (See previous post)

(3) Commutativity - For all a,b R, a+b = b+a and a*b = b*a

(4) Distributivity - For all a,b,c R, a*(b+c) = a*b + a*c and (a+b)*c = a*c + b*c.

(5) Identity - The set R contains and an additive identity element, denoted by 0 (identity for addition which is the first operation in our example) such that for all a R, a+0 = a and 0+a = a.

(6) Inverse - For each a R, the equations a+x = 0 and x+a = 0 have a solution x R, (x R, is read as x is a member of the set R) called the additive ( our first operation) inverse of a and is denoted as -a.

You can read more on this and ask your questions but to explain in respect in its simplest form; a Ring is Group with two operations, identity of the first operation, inverse of the first operation, and it obeys the axioms of a group plus its commutative and distributive.. Thats all on Rings for now.... Next up is Fields....

Richiez: @chibuzor, wise man! well i'v answered some questions on pigeonhole principle. buh i think, groups, rings, field e.t.c are more used terms when we talk of abstract algebra.pls can u explain wot these terms are?

A group is a set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms (Axioms are statements/facts that are undisputable (more or less)...). The Axioms are; (1) Closure, (2) Associativity (3) Identity, (4) Invertibility. Popular examples of Group is the INTEGER, NATURAL NUMBERS....
The above definition is from Google (Edited by me)

Illustration...
For a Group of Integers..
Two elements (3 and 4) operation +
3 + 4 = 7 and 7 is also a member of the group Integer (This fact is called Closure).

(3 + 4) + 5 = 3 + (4 + 5) = 12 (Associativity)

Identity element is that which when combined with another element in the group with an operation returns the latter element e.g 3 + 0 = 3 (0 is the identity element of addition). 3 * 1 = 3 (1 is the identity element for multiplication)

The illustration for Invetibility is simply too long to put here and i dont want to copy and paste.. please google it and ask question about it... Others are coming right up...

@Richiez... Yeah I ll do some explanation in the evening... I am at work at the moment...

Richiez: @chibuzor u'r highly welcomed, ur contributions wud be of great help.

I had huge problems with Real Analysis (Abstract Algebra) While in School, I had to do a lot of cramming to pass the exams. I studied later to catch up tho... I know a lot of people will have the same problem.

I am greatly impressed with what you have done here... I am interested in this thread... I want to get a job as a maths/f.maths teacher as soon as I am done with NYSC in the Ministry..... I will try to answer a few questions here myself... Thanks
Chibuzor...

Benitez..... Destroying European Champions since 2005....

Fuc.k Benitez

Thanks

Mod... update score pls..

HERNANDEZZZZZZZZZZZZ

Its so bad dat my first frontpage thread would be a tragedy..

Rumours flying around on BBM says the popular Yoruba actress Bisi Komolafe is dead. Can anyone confirm this?..

I love it when Chelshit falls apart...

The Subject is sooo Misleading...

Allowee Bus don enta.. I need a #200 change to make my #20,000 galant....

EFX001: lies lies lies lies lies, my sister is in kubwa as well. I just called her right now. She stays in block D and she just told me that nothing happened. I wonder who spreads all this nonsense. Fellow nairalanders, we need to find out those people that are determined to rubbish the name of our country.

Ur Sista wasnt honest with you.. Maybe she was busy Warming Cpt. Ijakpa's Bed when d robbery took place.... I stay in Bakassi A Block and I can tell u dat a robbery took place...

I am in FCT camp Kubwa too.. I heard of the Incident and was surprised that nothing was heard of d investigation.. All the soldiers know is to shout 'Double Up' 'Do Something'..

Abuja... Kubwa camp loadin........

Keke on the run nko? Saw it on playstore sometime ago but my SG-5300 isnt compatible...

dabrake: why is our presido stealing nigga raw's line nah(in love with an angel)?

It shows that he listens to our kind of music... See ur mouth like Cat-fish own....

I dont know about Azonto but the dance employed in Kukere is actually 'etighi'. And it is d traditional dance for SouthSouth pple of Nigeria. If u Komole or Rababa in Church as a Yoruba person, is it a sin?.... food for thought.