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CMSC434 Introduction to Human-Computer Interaction SAMPLE SOLUTIONS FOR EXAM 1 This solution set is by no means complete and extensive. This document s purpose is more to give you a general sense of the answers. Most of the answers required creativity so it would be very difficult to come up with a superset of all of the answers. If you exhibited knowledge and came up with reasonable solutions you most likely received credit. If you have any questions about the grading of your exam or would...

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Hi welcome to this tutorial on the binomial distribution now the aim of this tutorial is to show you what a binomial distribution is and the notation that we use now the binomial distribution has four properties and the best way of demonstrating this is by way of tree diagrams and the first tree diagram I'm going to show you is that of throwing a dart till you get a bull's-eye you can throw the dart into the dartboard you either get a bull's-eye or you don't and if you get a bull's-eye I'm going to stop throwing the dart, so I carry on to my second throw and I either get a bull's-eye or I don't get a bull's-eye and so on now I could keep throwing the dart at the dartboard and never in theory get a bull's-eye, so this tree diagram would go on and on and on forever and ever it would have what we call an infinite number of trials are these sections in between the dotted lines here they represent in this particular example the first so the second throw third throw and so on so what is the first property for a binomial distribution well it is that we have a fixed number of trials n and so this particular model would not fit a binomial distribution because as I say it's got an infinite number of trials so let's have a look at another tree diagram which has a finite number of trials a fixed number of trials and here's one we've got the playing of two football matches I've got my fixed trials each one represents a match this is the first match from the second match, and then you'll notice that what I've got here is that in any match you can either win it draw or lose and then if you've won say the first match you could go on to win the can match draw the second match or lose the second match and so on now what is the second property for a binomial distribution well the second property is that we should have two outcomes in a trial success or failure now in this particular tree diagram in say this trial here I haven't got two outcomes the outcomes are winning drawing or losing three outcomes, and you'll see in this trial here as well I haven't got two outcomes I've got three outcomes winning drawing or losing so this type of tree diagram is not suitable for a binomial distribution so remove that particular diagram, and we'll have a look at another one playing two games of tennis I've got a fixed number of trials n I've got two trials my first match my second match I've got two outcomes in a trial success or failure because in any match I can either win the match or lose the match now what is the third property for a binomial distribution well the third property is that trials are independent what does that mean well if I look at this trial here my second match I've written this particular notation and if you're not familiar with it what it means is that assuming that I won the first match this is about winning the next match given that I won the first match and the same down here we've got for this one if I won the first match this is about losing it...

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What is cmsc434?

CMS434 is a code for a course at the University of Maryland.

Who is required to file cmsc434?

Only students enrolled in the course CMSC434 are required to file cmsc434.

How to fill out cmsc434?

Fill out cmsc434 by following the instructions provided by the course instructors.

What is the purpose of cmsc434?

The purpose of cmsc434 is to teach students about user interfaces and interactive systems.

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The information that must be reported on cmsc434 includes assigned projects, progress updates, and final project submissions.