// Testing.cpp : Defines the entry point for the console application.

//

#include "iostream"

using namespace std;

int results[50];

long memoized_fibonacci_recurs(int results[],int n) {

long val = 0;

if (results[n] != -1)

return results[n];

if (n == 1)

val = 1;

else if (n == 2)

val = 1;

else {

val = memoized_fibonacci_recurs(results,n - 2);

val = val + memoized_fibonacci_recurs(results,n - 1);

}

results[n] = val;

return val;

}

long fib(int num)

{

if ( num == 0 )

return 0;

if ( num == 1)

return 1;

else

return (fib(num-1) + fib(num-2));

}

long memoized_fibonacci(int n) {

for(int i = 0; i < 50; i++)

results[i] = -1; // -1 means undefined

return memoized_fibonacci_recurs(results,n);

}

int main(int argc, char*argv[])

{

long num = fib(40);

long num1 = memoized_fibonacci(40);

cout << "Computed Value is:" << num << endl;

cout << "Memoized Computed Value is:" << num1 << endl;

}

## Monday, October 31, 2005

## Wednesday, October 26, 2005

### Maximum Likelihood

Let X=( ) be a random vector and

a statistical model parametrized by , the parameter vector in the parameter space . The likelihood function is a map given by In other words, the likelikhood function is functionally the same in form as a probability density function. However, the emphasis is changed from the to the . The pdf is a function of the 's while holding the parameters 's constant, is a function of the parameters 's, while holding the 's constant.When there is no confusion, is abbreviated to be .

The parameter vector such that for all is called a maximum likelihood estimate, or MLE, of .

## Monday, October 24, 2005

### Standard Deviation

Suppose we are given a population

http://en.wikipedia.org/wiki/Standard_deviation For formulaes

*x*_{1}, ...,*x*_{N}of values (which are real numbers). The arithmetic mean of this population is defined ashttp://en.wikipedia.org/wiki/Standard_deviation For formulaes

## Monday, October 17, 2005

### Probability Distribution function

Random variables: Are the real valued functions defined on the sample space i.e they map the outcomes of an experiment from a non-real outcome to real numbers outcome.

Analogy: For e.g while tossing a dice we are not interested in the actual outcomes but are interested in the functions of the outcome

A random variable that can take at most a countable number of possible values is said to be discrete. For discrete random variable we define probability mass function

Picked from lecture notes :) for my reference ( thanks to whoever did it)

Cumulative Distributive function

--------------------------------------

What is the probability that x is less than or equal to x0?

The probability that x < x="-" infinity="" integral="" x0="" dx="">

This integral yields the area under the curve between x = -∞ and x = x0

and is called the cumulative density function or cdf denoted by ‘g’.

Analogy: For e.g while tossing a dice we are not interested in the actual outcomes but are interested in the functions of the outcome

A random variable that can take at most a countable number of possible values is said to be discrete. For discrete random variable we define probability mass function

Picked from lecture notes :) for my reference ( thanks to whoever did it)

Cumulative Distributive function

--------------------------------------

What is the probability that x is less than or equal to x0?

The probability that x < x="-" infinity="" integral="" x0="" dx="">

This integral yields the area under the curve between x = -∞ and x = x0

and is called the cumulative density function or cdf denoted by ‘g’.

•Variance – measure of the deviation from the mean for points in one dimension e.g. heights

•

•Covariance as a measure of how much each of the dimensions vary from the mean with respect to each other.

•

•Covariance is measured between 2 dimensions to see if there is a relationship between the 2 dimensions e.g. number of hours studied & marks obtained.

•The covariance between one dimension and itself is the variance

Covariance Properties

---------------------------------

Covariance Properties

---------------------------------

•Exact value is not as important as it’s sign.

•A

__positive value__of covariance indicates both dimensions increase or decrease together e.g. as the number of hours studied increases, the marks in that subject increase.•A

__negative value__indicates while one increases the other decreases, or vice-versa e.g. active social life at RIT vs performance in CS dept.•If

__covariance is zero__: the two dimensions are independent of each other e.g. heights of students vs the marks obtained in a subjectCovariance calculations are used to find relationships between dimensions in high dimensional data sets (usually greater than 3) where visualization is difficult

variance (X) = Σi=1n(Xi – X) (Xi – X)

(n -1)

covariance (X,Y) = Σi=1n(Xi – X) (Yi – Y)

(n -1)

•the mass (probability) of a small section of wire is the mass per unit length (density) times it length of section (bin width) under consideration.

### Analysis Server Database Backups

The backup extensions for analysis server are .abf, you connect to the analysis server database and right click on it to restore a database with .abf extension to restore the database.

Dunno what i wrote :)

-Kalyan

Dunno what i wrote :)

-Kalyan

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