^{nd}Nov 2022

# MTH219 Fundamentals Of Statistic And Probability Assignment Sample Singapore

MTH219 Fundamentals of Statistics and Probability is a college-level course that introduces students to the basic concepts of statistics and probability. The course covers a wide range of topics, including data collection and analysis, statistical inference, and probability models. In addition, the course emphasizes the use of statistical software to perform analyses and interpret results. Whether you are planning to pursue a career in statistics or simply want to learn more about this fascinating subject, MTH219 is the perfect place to start.

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In this section, we’ll describe some assignment briefs. These are:

**Assignment Brief 1: C****alculate the expectation, variance, and median of any random variables.**

Random variables are an essential tool in many fields, from mathematics and physics to finance and computer science. By definition, a random variable is a function that assigns a numerical value to each outcome of a random event. The expectation of a random variable is its average value, calculated over all possible outcomes.

The variance of a random variable is a measure of how to spread out its values; it is calculated as the expectation of the squared deviation from the mean.

Finally, the median of a random variable is the value that divides the distribution of values into two equal halves. These three measures – expectation, variance, and median – provide valuable information about any given random variable.

**Assignment Brief 2: Determine the probability of events.**

Probability is the measure of how likely an event is to occur. It is usually expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. Probability can be calculated using a variety of methods, including counting, probability trees, and simulations.

Often, a simple formula can be used to determine the probability of an event occurring. For example, if a coin is flipped five times and lands on heads three times, the probability of heads can be calculated as 3/5. This means that, on average, the coin will land on heads three out of every five flips.

In general, the more data that is available, the more accurate a probability calculation will be. However, even with a small amount of data, it is still possible to make reasonable estimates of probability.

**Assignment Brief 3: Demonstrate the dependence or independence of the events.**

In statistics, two events are dependent if the outcome of the first event has an impact on the outcome of the second event. For example, if you roll a die and then roll a second die, the outcome of the second roll is dependent on the outcome of the first roll.

However, if you roll two dice simultaneously, the outcomes of each roll are independent. This is because the outcome of one role does not affect the outcome of the other. In other words, independence is when two events are not related.

So, when we say that two events are independent, what we really mean is that the probability of one event occurring is not affected by whether or not the other event occurs. We can demonstrate this using a simple coin flip experiment.

If we flip a coin twice and get two heads, we would say that the probability of getting two heads in a row is 1/4 because there is a 1/2 chance of getting heads on the first flip and a 1/2 chance of getting heads on the second flip. However, if we were to flip two coins at the same time and got two heads, we would say that the probability of getting two heads is 1/2*1/2=1/4 because each flip is independent of the other. As we can see, independence has a big impact on probability.

**Assignment Brief 4: Able to give an opinion about the results acquired by the direct calculation of the probability of events v/s those gained by Normal/Poisson approximation.**

Many people believe that the Normal and Poisson approximations are more accurate than the direct calculation of probability. However, this is not always the case. In some situations, the Normal and Poisson approximations can be quite inaccurate. For example, if the events are not evenly distributed, the approximations can be off by a significant amount.

Additionally, if the events are rare, the approximations can also be less accurate. In general, the more data you have, the more accurate the approximations will be. However, in some cases, the direct calculation of probability can be more accurate than the approximations.

**Assignment Brief 5: Implement the probability models into practical settings.**

Probability models are mathematical models that aim to quantify the underlying likelihood of an event occurring. They have a wide range of applications, from predicting future stock market movements to determining the chances of winning a game of poker. While probability models can be complex, they can be extremely powerful tools for understanding and predicting the likelihood of events occurring.

When implemented in practical settings, they can help us make better decisions and improve our chances of success. For example, by understanding the probability of certain events occurring, we can make more informed investment decisions, choose which insurance policies to purchase, and develop strategies for dealing with risk. Ultimately, probability models can help us to navigate the world around us more effectively and make more informed choices.

**Assignment Brief 6: Ascertain statistical information of a given data set.**

There are many ways to ascertain statistical information from a given data set. One of the most common is to calculate the mean, median, and mode. The mean is simply the average of all the values in the data set. The median is the value that falls in the middle when all the values are sorted from smallest to largest.

The mode is the value that occurs most often in the data set. Other ways to analyze data sets include calculating the range, standard deviation, and percentiles. Each of these methods can provide valuable insights into the nature of a data set.

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