The Probability Density Function is a function that gives us the probability distribution of a random variable for any value of it. To get the probability distribution at a point, you only have to solve the probability density function for that point.

The cumulative distribution function is used to describe the probability distribution of random variables. It can be used to describe the probability for a discrete, continuous or mixed variable. It is obtained by summing up the probability density function and getting the cumulative probability for a random variable.

The cumulative distribution function of a random variable to be calculated at a point x is represented as Fx(X). It is the probability that the random variable X will take a value less than or equal to x.

Consider the diagram shown below. The diagram shows the probability density function f(x), which gives us a rectangle between the points (a, b) when plotted. f(x) has a value of 1/(b-a).

Now consider a point c on the x-axis. This is the point you need to find the cumulative distribution function at. According to the definition, you need to find the total probability density function up to point c. This means that you have to find the area of the rectangle between points a and c.

Since the cumulative distribution function is the total probability density function up to a certain point x, it can be represented as the probability that the random variable X is less than or equal to x.

Figure 4: CDF representation

As you need to get the total PDF sum between two points, you can also represent the CDF as the integration of PDF between the points it has been calculated at. The formula depicted below shows the cumulative distribution function calculated between points (a, b) for the PDF Fx(x).

Source – simplilearn,com

The software-reuse is a process of reusing “the software designed for reuse purpose”. Software-reuse is the solution that avoids a repeated labor in the software development and can make use of the knowledge and experience getting from the past software development and concentrates the especial part of application. It’s aim is making the software development from zero no longer. Software reuse is the process of creating software systems from existing software rather than building software systems from scratch. Anything that is produced from a software development effort can potentially be reused. Software reuse is the process of implementing or updating software systems using existing software assets. A good software reuse process facilitates the increase of productivity, quality, and reliability, and the decrease of costs and implementation time. An initial investment is required to start a software reuse process, but that investment pays for itself in a few reuses

Software-reuse can be divided into product reuse and process reuse according to the reuse object. Software-reuse can be divided into product reuse and process reuse according to the reuse object. The product reuse means the reuse of software component, getting a new system from component integration and construction. The process reuse means the reuse of past software development process, automatically or half-automatically producing the system using the reuse generator. The process reuse depends on the applicable to some special applied domain currently, but the product reuse is a realistic and essential path now.

PROCESS OF SOFTWARE-REUSE

1. Domain Analysis Phase: This phase is to come certain whether deserve to reuse the infrastructure for the domain development mainly through the definition and analysis of application domain.
2. Domain Engineering Phase: This phase is to acquire general system structure according to the domain commonness getting from domain analysis phase and regulate how the property match the system structure and how to bind variable point.
3. Property Obtaining Phase: This phase includes development of reuse, may also includes some exterior adopt of reuse property.
4. Property Categorizing Phase : This mission is a database management mission actually, including categorizing and saving reuse property.
5. Property Maintaining Phase : This mission is a maintenance mission actually, and to combine configuring management and edition control.

Advantages of software reuse:

• Less effort: Software reuse requires less effort because many components use in the system are ready made components.
• Time-saving: Re-using the ready made components is time saving for the software team.
• Reduce cost: Less effort, and time saving leads to the overall cost reduction.
• Increase software productivity: when you are provided with ready made components, then you can focus on the new components that are not available just like ready made components.
• Utilize fewer resources: Software reuse save many sources just like effort, time, money etc.
• Leads to a better quality software: Software reuse save our time and we can consume our more time on maintaining software quality and assurance.

Q1.State t-test and its applications for small samples.

Answer:       Follow the below link for answer:

State t-test and its applications for small samples.

Q2.A computer while calculating correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results : n=25, ∑ X= 125, ∑ X^2=650, ∑ Y=100, ∑ Y^2= 460, ∑ XY =508. If was, however, later discovered at the time of checking that he had copied down two pairs as (X,Y)= (6,14),(8,6) while the correct values were (X,Y)=(8,12),(6,8).

Obtain the correct value of correlation co-efficient.

Answer: Follow the below link for answer:

A computer while calculating correlation coefficient between two variables X …

Q3.Fit the Exponential Curve y= a e^(bx) for the data x: 1, 2, 3, 4, 5 and y : 1.5, 4.5, 6, 8.5, 11 .

Answer:   Click here to get answer —->exp curve fitting

Q4.If the regression coefficient are 0.8 and 0.2 , what would be the value of coefficient of correlation?

Answer:

Let rx=0.8, ry=0.2
Coeff. of correlation=Geometric Mean of Regression Coeff.
=√(0.8 x 0.2)
=√(0.16)

= 0.4

Coeff. of correlation = 0.4