Introduction

A data has the topics of the similar information which are using for some distribution. Data distribution has nothing but a data is multiple and dividing by a single data. We have to see some of the data distribution with more detailed explanation in the followings. Also we can see the different types of the data distribution with examples in them.

Types of Data Distribution Using:

The followings are different types of data distribution using.

Types of Data:

Data are two different types as qualitative and quantitative as shown below.

A qualitative data has a categorical measurement and a specific format with expression of number.

A quantitative data has a numerical measurement that can be represent with the number in them.

Types of Distribution:

In this we can see two different types of distribution.

Poisson distribution.

Binomial distribution.

Examples for Data Distribution Using:

The followings are examples for data distribution using.

Poisson distribution:

The formula for calculating a Poisson distribution is f (x) = ‘(e^-m m^x)/(x!)’

The mortality rate for a certain disease is 4 per 1000. We have to find the probability for the 5 deaths from this disease in a group of 500?

Solution:

p = ‘4 / 1000’ = 0.004

m = np = 500(0.004)

= 2

f(4) = ‘(e^-2(2)^5)/(5!)’

= ‘((2.7183)^-2(2)^5)/(5!)’

= ‘ ((0.7183) 32)/(5!)’

= ‘22.9856/(5!)’

= 0.1915

Binomial distribution:

Four cars are drawn from a lot of six cars containing two effective cars. We can find the probability distribution for the number of defective cars in them.

Solution:

Let x be a random variable denotes the number of defective cars

Probability of defective car selected is

p = ‘2/4’ = ‘1/ 2’

q =1-p = 1′-1 / 2′ = ‘1 / 2’

By Binomial distribution

P( X = x ) = nCx px qn-x

The given problem in that n = 4 & x = 0,1,2,3

P(x= 0) = 4C0 (‘1 / 2’ )0 (‘1 / 2’ )4 = ‘1 / 16’

P(x = 1) = 4C1 (‘1 / 2’ )1 (‘1 / 2’ )3 = ‘1 / 8’

P(x = 2) = 4C2 (‘1 / 2’ )2 (‘1 / 2’ )2 = ‘1 / 4’

P(x = 3) = 4C3 (‘1 / 2’ )3 (‘1 / 2’ )1 = ‘1 / 2’

Therefore, the Probability distribution is

Data integration is one of the type of integration process. In this data integration, we use different data values. Integration is used for finding the some particular area of the curve. Integration of a function is denoted as G(x), R(x). Here x is the given function. There are different limits are used in integration process. The limits are used for finding the area of the particular region.

General formula for data integration:

? k dx = kx + c

? xn dx = x(n + 1) / (n + 1) + c

? udv = uv – v ? du

Example problem for data integration:

Data integration example problem 1:

Integrate the given data value ? (14x + 7×6 – 8×2) dx

Solution:

Integrate the given data with respect to x, we get

? (14x + 7×6 – 8×2) dx = ? 14x dx + ? 7×6 dx – ? 8×2 dx

= 14 (x2 / 2) + 7 (x7 / 7) – 8 (x3 / 3)

= 7×2 + x7 – (8 / 3)x3 + c

Answer:

The final answer is 7×2 + x7 – (8 / 3)x3 + c

Data integration example problem 2:

Integrate the given data function ? (15×4 – 6×2 – 8×3 + 4) dx

Solution:

Integrate the given data with respect to x, we get

= ? 15×4 dx + ? 6×2 dx – ? 8×3 dx + ? 4 dx

= 15 (x5 / 5) + 6 (x3 / 3) – 8 (x4 / 4) + 4x + c

= 3×5 + 2×3 – 2×4 + 4x + c

Answer:

The final answer is 3×5 + 2×3 – 2×4 + 4x + c

Data integration example problem 3:

Integrate the given data ? (sin8x) (sin4x) dx

Solution:

Rearrange the given data,

SinA sinB = (cos (A – B) – cos (A + B)) / 2

From given data, A = 8x, B = 4x

Sin (8x) Sin (4x) = (1 / 2) * (cos (4x) – cos (12x))

Substitute the above values in the given data, we get

Therefore,

? (sin8x) (sin4x) dx = ? (1 / 2) * (cos (4x) – cos (12x)) dx

= (1 / 2) [ ? cos (4x) dx – ? cos (12x) dx]

= (1 / 2) * [ (sin 4x / 4) – (sin 12x / 12)] + c

= (sin 4x / 8) – (sin 12x / 12) + c

Answer:

The final answer is (sin 4x / 8) – (sin 12x / 12) + c

Practice problems for data integration

Date integration example 1:

Integrate the given function ? cos4x dx

Answer:

The final answer is (1 / 32) * (12x + 8 sin (2x) + sin (4x))

Data integration example 2:

Integrate the given data ? (19×2 – 5×6 + 62x) dx

Answer:

The final answer is (19 / 3)x3 – (5 / 7)x7 + 31×2 + c