The Complete Guide To Expectation And Variance For Some Random Variables In Probability

Expectation And Variance For Some Random Variables
January 27, 2021
Author : Warren Armstrong

In probability, there are two vital theories that play an integral role in deciphering the crucial concepts associated with writing a statistics assignment. They are the theory of continuous random variables and the theory of discrete random variables. Both of these theories concern a set of random variables. The primary task involves determining the expected values using these theories and then finding the variance. This is the basic crux of what students are generally expected to calculate in these technical assignments.
Do you find yourself sailing on the same boat? Not to worry, our experts who have been providing high-quality statistics assignment help in Canada have been trained in such a way that it doesn’t take us more than a few moments to prepare reliable reference assignment solutions for students to rescue them out of all their assignment-related queries. Over the years, we have fulfilled our motto of “making assignments simpler” for students.

There are some similarities between the theory of discrete random variables and the theory of continuous random variables. It is just that the summations and PMFs in one of these get replaced with the integrals and PDFs. Therefore, there are similarities in the way of approaching the probability assignment questions on the theory of discrete and continuous random variables.

There’s a lot that these crucial topics in probability offer to students; with an abundance of formulas and calculations, it often becomes a burden to get away with solving these complicated assessments for them. This is where our experienced and professional writers step into the scene and guide them through all their problems within a jiffy. If you’re wondering how we do it, then you must hover to our wide range of samples that have been curated specially for the reference purpose of students in these years. For now, let us give you a quick knowledge of expectation and variance for random variables.

How is variance related

Expectation And Variance In Statistics: A Closer Look!

For the last few years, we have seen a lot of students wandering for some credible solutions to their probability and statistics assignment problems. Since then, our probability assignment help writers have been engaged in harnessing all their years of experience and diverse knowledge in producing impeccable results in this field of study for them.

Our speciality is that we do not leave even a single stone unturned for you. We begin from the starting and cover all the concepts that you would be needing while solving such assignments. Therefore, before we take you around one of our best-solved assignments, it is time that we give you a brief overview of expectation and variance in probability. After this, you will understand the sample better.

Expectation and variance are two of the most essential sections of statistics. If we are given any random variable, most of the times, it is expected to calculate the expectation and variance for that variable. While the average value of the given random variable is known as the expected value or expectation for the random variable, the spread of variability around the expected value is termed as the variance. The expectation can also be termed as the long-term average for a random variable.

Mathematically expressing this, the expectation of a random variable can be expressed as:

expectation of a random variable 1

Similarly, the variance of a random variable can be expressed as:

expectation of a random variable 2

Now that you are familiar with the formulas for both of these, it is vital for you to study some of the properties of expectations and variance, before we give you an overview of how to solve a probability assignment on them.

Properties Of Expectations For A Random Variable

As discussed, our experts who provide students with reliable statistics assignment help in Canada do not leave any topic untouched for them while guiding them on the assignments. Therefore, now we will help you in understanding the properties of expected value for a random variable which will concrete your knowledge on this topic.

These are:

  1. If g and h are the two functions, and there are two constants a and b, then for any given random variable X, irrespective of whether it is discrete or continuous, E(aX+b)=aE(X)+b
  2. If there are two given random variables X and Y, then

E(X+Y)=E(X)+E(Y)

  1. If there are two given random variables X and Y that are independent and have g and has their functions, then

E(g(X)h(Y))= E(g(X))E(h(Y))

These are some of the properties of expectations that you need to know before proceeding with the assessments that cover this topic. If you get stuck with understanding any of these, then you can always come up to our statistics assignment help experts or guidance on them. You can even consult us via the interactive face-to-face sessions that we hold for you all throughout the day for instant feedback from us.

Now let us move ahead with discussing the properties of variance in probability.

Properties Of Variance For A Random Variable

For a better understanding of the assignments that come your way covering this topic, it is a must for you to be thorough with the properties of variance as well. In the last decade, students have relied upon our experts for affordable statistics assignment help in Canada. Knowing the hardships that students face while taking assistance from an expert, we have revamped all our prices to suit your budget better.

For now, let us throw some light on the properties of variance in probability

  1. If there is a random variable X and it has a high variance, then the value for its variance will be a long way from the mean.
  2. If there is a random variable X and it has a low variance, then the value for its variance will be in a clustered form, near and around the mean value.

We hope we have been able to give a brief knowledge of the properties of expectation and variance in this section. Now, it is the perfect time for us to introduce you to the probability questions that our statistics assignment help experts have been covering in this area of study for the last few years. As you have got an overview of the concepts included in these assignments, you will now be able to relate with them better. So without further ado, let’s get started.

How To Solve A Statistics Assignment Problem On Expectation And Variance? Here’s How We Do It!

There is a wide range of questions that students get on this topic in probability. Fortunately, our industry veterans have been through with all of them and covered them all for them. Amidst them, there are some of the questions that we have received over and again. Owing to their importance, our experts who provide statistics assignment help in Canada will now be sharing a brief approach on them. With the help of a few excerpts from the solution that has been curated by us, it would be easy for you to understand it better.

expectation of a random variable 3

As you can see in the image above, this is an assessment brief for the questions that students get for this assignment. Adhering to these, let us now give you a glimpse of the questions that students sent our statistics assignment help experts.

expectation of a random variable 4

As shown in the image above, these are the questions that have been covered by us over and again. Let us discuss the first question and show you how to solve it.

The main objective of the question is to show that Y(1) has the value of its distribution as an exp (nƛ). This is how we prove it.

expectation of a random variable 5

These are some of the steps that are carried out by our statistics assignment help experts to reach the answer. The calculations are quite lengthy and demand an enormous time and effort from students, which is why it renders students helpless at the end. To cut it short, we have already done every bit from our end.

By applying all the appropriate formulas, this is how we fulfil the objective of this question.

expectation of a random variable 6

In the same way, we have also provided instant solutions to all the questions that students have brought to us all over the world. Due to the extensive knowledge that we possess, we have become the leading organisation for statistics assignment help in Canada.

How Our Statistics Assignment Experts In Canada Help Students In Combating All The Queries On These Technical Assessments?

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About the Author

Warren Armstrong

Warren Armstrong is a professional statistician who has worked with the Australian Bureau of Statistics for a long time, then became a private tutor before he was a statistics assignment writing expert at My Assignment Services. He has published several works in the field of statistics before shifting to assignment guidance. He offers help and consultation to the students for writing their assignment in the form of tips, explanation of complex topics, resolving queries and providing live sessions. Warren has helped a number of students with their assignments.

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