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Probability: It explained uncertainty of any event, and arise question about that event how much time they will occur, Such as we can take an example of any natural disaster like how many times earth will hit by any asteroid in next 30 years, then what you think may be one or two or three or may be never. This is the probability. It is never show certainty of any event and also shows randomness.

It is quit complex but you will simply recognized them by following these points:

  • It shows multiple interpretations.
  • Nuts and bolts are simple probability mumbo jumbo: sample space, events, probability function etc.
  • How to count.
  • Bayes Rule and how it can relates to the subjective probability matter
  • What is the meaning of randomness

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Sample Spaces: When any random experiment is done, then all possible outcomes of experiment is known as sample space. This experiment is done with two ways one is Random, and another is Deterministic. Random show uncertainty, some examples like rainfall measurement, coin toss event etc.

Events: E is event which is a collection of outcomes or we can say that it represents subset of sample space. When event E occur then collection of events are E1, E2, E3..En are disjoint.

Properties of Probability:

  • Function: All events are attached with probabilistic function rule. Such as event function of event E is
  • IP(E) = p it is probability of event E. Any function can fulfill following rules
  • IP (E) 0 for any event E S .
  • IP(S) = 1

Laws for Probability:

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  • Multiplication law:
  • Addition law:

Two Discrete Random Variables:

  1. The probability mass function (pmf) of a single discrete rv X specifies how much
    probability mass is placed on each possible X value.

  2. The joint pmf of two discrete rvs X and Y describes how much probability mass
    is placed on each possible pair of values (x,y).


It concerns about data collections, analysis and their interpretations. Here I am going to explain about two types of statics.

Descriptive: It explained data summarization. In this type of statistics calculating number of data will measures for example percentages, sums, averages etc. It means data sets will describe through multiple ways. These categorized data is represented by frequencies and relative frequency to get some idea about these different type of data category. It depends upon types of data and data is categorized into these types:

  • Quantitative data : It shows measurement of quantity on observational value.
  • Qualitative data : Shows quality and property of data.
  • Logical data : It show true or false statement of data, it is the most important type of data.
  • Missing : data must be there but are not.

Inferential: It work greater than descriptive by including inferences with sets of data.

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