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The document discusses important concepts and formulas related to applied mathematics including numbers, modulo arithmetic, congruence, alligation,
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where P(X = xi) i.e. pi lies between 0 and 1, and pi, = 1.  180 pages
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E(X) =  Variance = ()(()) Standard deviation =  √

= 4 pages

Binomial distribution You're Reading a Preview 100% (1)

It is represented by (q+p) n
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or B(n,p) and P(X=r)=   − where r = 0, 1, 2, ….. n
Antilock Brakes

Mean, variance and standard deviation of binomial distribution :

mean = = np  , variance =  = npq Upload to Download

, standard deviation σ =  118 pages

POISSON DISTRIBUTION: No ratings yet

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The poisson distribution is the limiting form of Binomial distribution when no. of trials is very large
OR
() = ! −
Mean and Variance of Poisson Distribution
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 =   =  , , standard deviation σ = √ No ratings yet

Normal Distribution Start your 30 day free trial
Micro Lec
It is used for Continuous random variable . It is also called Gaussian distribution. It is a bell shaped curve
symmetric about a vertical line through the mean. For Normal distribution curve Mean = median = mode

normal density function () = √ − () , ∞ <  < ∞ 17 pages

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Standard Normal Distribution
Algebraic Laws of Regular Expressions:
If  = 0,  = 1 said to have standard normal probability distribution. The random variable in case of standard
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() = √12 − , ∞ <  < ∞, z =   13 pages

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  ̅ = Σ ,       () = Σ( −1̅) 4 pages

⁄. √
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The interval estimation of population mean is given by μ=x ± margin of error Defined by The People

Mean of random sample drawn from any distribution with mean μ and variance σ2 will have an approximate
normal distribution with a ̅ = μ and s2 =
√ . So s =
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Standard error of mean =

√
Hypothesis Testing
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Type 1 error : H0 Reject UploadType

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2 Error : H0 Acceptto download.

Null Hypothesis (Ho) Alternative Hypothesis (Ha) 34 pages

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1. There is no difference between a parameter 1. Existence of a difference between a No ratings yet
and a specific value or there is no difference parameter and a specific value or states that Efficiency of Horizontal Drains On Slope
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2. Two groups studying are same. 2. Two groups studying are different.
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Degree of freedom:-
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For one sample test DF = n-1 , For two sample test DF = n1+n2-2 Mplementation of Cavitation Models Into
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 =  ̅−⁄√  = ⁄ ̅√−− ,
themultiphaseEulerFoam Solver

̅ =  ,  =    = ℎℎ     35 pages

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Two Sample t-test

: = (    ) No ratings yet

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: ≠ (     )
 = ( ̅−+ ̅)  = ( ̅−+ ̅) ℎ  = (− ̅)++(−−) (−)++(−−)
or or s =
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 
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Additive Model : O = T+C+S+L
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Multiplicative Model : O = T x C x S x L

Method of Moving Average Upload to Download No ratings yet

Method of Least squares :: Aej S 23 02916

1. The sum of the deviations of the actual values of y and yi (estimated value of y) is zero
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 (y-yi )= 0
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2. The sum of squares of the deviations of the actual values of y and yi (estimated value of y)
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is least   (y-yi )2 is least
Universidad Politecnica Metropolitana
For the purpose of plotting the best fitted line for trend analysis, the real values of constants ‘a’
de Hidalgo: Name: Luis Daniel Salas Soto
and ‘b’ are estimated by solving theStart your 30two
following dayequations:
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 Y=na+b X ------------ (ii)  XY = a  X + b  X2 --------- (iii)
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2. When X = 0, the equations (ii) and (iii) reduce to:
Y = na + b (0)  a= And, XY = a (0) + b X2  b= No ratings yet
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the trend line of best fit : yt = a+bx

Financial Mathematics
61 pages
perpetuity::

• P=
 When periodic payment is made at the end of each payment period.,

• P=R+
 : When periodic payment is made in the beginning of each payment period.

Sinking Fund :

• A=R (+) − or A = R. / If payment made at the end of each year

• A=R (+) − (1+i) or A = R( +/ -1) If payment made in the beginning of each year then

EQUATED MONTHLY INSTALLMENT (EMI)

flat rate method

EMI =
+
  EMI =
+ ,I=


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REDUCING BALANCE METHOD

EMI =
 (+)
  (+)
−
 You're
or EMI = Reading
   
−(+) aorPreview
EMI =
/
Amortization Formulas Upload your documents to download.

Principal outstanding at beginning of kth period =

[(+) −]
(+)Download
 or EMI. −+
 /
Upload to
Interest paid in kth payment =
[(+)
(+) −]
 −+/ or EMI. i.

Principal paid in kth payment - EMI - Interest paid in kthOR

period

Total interest paid = n x EMI-P

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Return on investment

Rate of Return =
 /
   100 Start your 30 day free trial

re = ((1 +
 )p – 1) Where re is the effective interest rate

if interest is compounded continuously , then Effective rate of return = (er – 1)

Compounded Annual Growth Rate (CAGR): CAGR = ⁄ 1

Depreciation: (i) Linear or Straight Line Method

Annual depreciation =
Usefullife ofasset
−
in years  − = ,

(ii) Written down value method : S = P(1-i)n

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