Probability and statistics Assignment Help




homework assignment help is most useful online portal for students providing all type of Online Probability and statistics assignment help Services. These are the separate articles on probability or the article on statistics. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is of mostly mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.

Probability and Statistics:

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. Statistics is the science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation.

                                                                                                                                                                                        

A Course in Probability and Statistics - Probability Course:

  • Course 1 - Probability Experiment:

         We can produce the experiment with a well defined outcome and this outcome is the solution for these experiments.

  • Course 2 - Event:

         It is an outcome of an experiment in random, which has the subset of a sample space.

Examples for probability:

The following examples show the probability course.

  • In a table, there are 20 books, 25 bags, and 5 pencil box. From table the bag is taken at random . After replacing it, second pencil box is taken. What is the probability of taking a bags and pencil box?

Solution:

P (bags) = 25/50

               = 5/10

P (pencil box) = 5/50

                       = 1/10

P (bags and pencil box) = P (bags) · P (pencil box)

                                      = 5/10 * 1/10

                                      = 5/100                      

                                      = 1/20

  • In a bag there are 5 cakes, 1 pups and 4 biscuits. Find the probability of choosing cakes without looking in the bag?

Solution:
P(choosing a cakes) = 5/10

                                 = 1 / 2

                                 = 0.5

                                 = 50% 
In this, numerator is 5 because we have 5 cakes in the bag and 5 outcomes. Therefore total number of outcomes = 10.

A Course in Probability and Statistics - Statistics Course:

The following examples show the statistics course.

  • Course 1 - Arithmetic mean:

          In statistics, the arithmetic mean is an average of data in arithmetic. A set of data which is dividing by sum of observations and number of observations in the given data.

                                  Sum of observations
Arithmetic Mean = ----------------------------------
                                Number of observations

  • Find the arithmetic mean of weights for 8 peoples in kilograms are 55, 20, 75, 82, 18, 33, 71, and 40.

Solution:

                                      Sum of total number
 Arithmetic mean = -----------------------------------
                                          Total number

                           = (55 + 20 + 75 + 82 + 18 + 33 + 71 + 40)/8

                           = 394/8

                           = 49.25

  • Course 2 - Standard Deviation:

      It is an arithmetic figure which has spread of data in variability and has values of root mean square in the arithmetic mean.    

  • Find the Standard deviation for 2, 4, 6, 9 and 14.

Solution:

Step 1:

Find the mean and deviation.

          X = 2, 4, 6, 9, 14

         M = (2 + 4 + 6 + 9 + 14)/5

            = `35/5`

      M   = 7

Step 2:

Find the sum of (X - M) 2

X

X-M

(X-M)2

2

4

6

9

14

2-7 = 5

4-7 = 3

6-7 = 1

9-7 = 2

14-7 = 7

25

9

1

4

49

 

total

88

Step 3:                                                                                      

    N = 5, the total number of values.

       = N - 1.

       = 5 - 1

       = 4

Step 4:

By this method we can locate the standard deviation. 

               = `(sqrt88)/(sqrt4)`                                                                 

               = 9.380 / 2

               = 4.690

probability and statistics learning

A probability distribution determines the probability of the value of discrete random variable or the probability of the value declining within an exacting continuous interval. Statistics is the science that learning a creation use of numerical data connecting to groups of individuals or an experiment. It refers about all aspects of statistics, which includes not only the gathering, examination and breakdown of such facts and also the preparation of the collection of data, in conditions to propose of an experiment.

An Event Takes Place in Probability and Statistics Learning

The dependent or independent variables terminologies are used more extensively than just in relation to prohibited the experiments. Independent variables are those that are interrupted where the dependent variables are only measured.

  • The probabilities of two independent events (A and B) are multiply the probability of the initial event by the probability of the next event.

                            P(A n B) = P(A) . P(B)

  • The probabilities of two dependent events (A and B) are multiply the probability of A and the probability of B after A occurs.

                            P(n B) = P(A) . P(B following A)

  • The probabilities of one or other of two mutually exclusive events (A or B) are adding the probability of the initial event to the probability of the next event.

                            P (A u B) = P(A) +  P(B)

  • The probabilities of one or the other of two inclusive events (A or B) are adding the probability of the initial event to the probability of the next event and subtract the probability of both events happening.

                            P(u B) = P(A) + P(B) - P(A n B)

Example for Probability and Statistics Learning

Problem: A business needs to estimate the true mean annual income of its customer. It randomly samples 150 of its customer. The mean annual income is 60,000 with a standard deviation of 1,250. Using statistical method find a 95% confidence interval for true mean annual income of the business customers.

      Solution:

              n = 150

        Sample:                                                   

              Mean = 60000

              Standard deviation = 1250

              Use z*

              Standard deviation becomes 1250/sqrt (1500) = 102.12

              z* at 95% confidence level = 1.96

              60000 +/- 1.96x102.12 or

              60000 +/- 200.15

      Answer: 59799.85 to 60200.15

Help with probability and statistics:

The probability should be the way of help with conveying the knowledge that the event will happen or happened. The probability of the event M should be the ratio of number of ways event M happen and total numbers of probable outcomes. Statistics could be help with the formal science which is creating valuable use of arithmetical operations. In this article we are going to see about the example for probability and statistics.

Example for Probability:

In a shop, there are 24 gold rings, 16 silver rings and 12 platinum rings. Find the probability of getting gold ring and platinum ring?

Solution:

Given, Gold rings = 24

          Silver rings = 16

          Platinum rings = 12

So, Number of total outcomes in this problem should be,

                     24+16+12 = 52

Total number of gold rings = 24

Therefore, the probability of getting gold ring = (24)/(52) = (6)/(13)

Total number of platinum rings = 12

Therefore, the probability of getting platinum ring = (12)/(52) = (3)/(13)

This is an example problem that help with probability.

Example for Statistics:

Find the mean, median and range for the following numbers,

51,33,14,17,25,60,56

Solution:

The given collection of numbers is,

         51,33,14,17,25,60,56

Finding Mean:

The formula for measuring the mean value is,

img

Here, Sum of all the given numbers = 51+33+14+17+25+60+56

                                                    = 256

Total number of given numbers = 7

Since, Mean = (256)/(7) 

                   = 36.57

Finding Median:

First we need to sort the given numbers. That is,

                14,17,25,33,51,56,60

Total number of given numbers = 7

That means, this should be an odd number.

So, Median = Middle number in the sorted list of numbers

                  = 33

Finding Range:

For finding the range value, we need to know which is the biggest value and smallest value.

From given, Biggest value = 60

                  Smallest value = 14

Thus, Range = 60 – 14

                   = 46

Answer:

Mean = 36.57

Median = 33

Range = 46

This is an example problem that help with statistics.



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