5. If you want to know how important spam filters are to your online experience, try turning them off for a day. You’ll quickly see why these tools we tend to take for granted are so essential. Generally speaking, a filtering solution applied to your email system uses a set of protocols to determine which incoming messages are spam and which are not. What the filters checks on can vary, but often they all do basically the same thing: scan header information for evidence of malice, look up senders on blacklists of known spammers, and filter content for patterns that point to junk mail. Suppose that a particular spam filter uses a points-based system in which various aspects of an email trigger an accumulation of points – with 100 points being the maximum and strongly indicating spam. So, more points for a particular email becomes stronger evidence that it is spam. After accumulating a sufficient number of points, the spam filter classifies the email as spam and it does not reach your inbox. This process is similar to hypothesis testing in the following way for each email it reviews: Họ: The email is a real message (not spam) HẠ: The email is spam Using the above hypothesis setting context, answer the following questions using language/terms we have covered related to hypothesis testing: a) When the filter allows spam to slip through into your inbox, which kind of error is that? Explain in terms of the hypotheses above. b) Which kind of error is it when a real (i.e., non-spam) email gets classified as spam and does not get to your inbox? Explain in terms of the hypotheses above. c) Suppose that this particular spam filter classifies spam as any email getting 50 points or higher. However, you reset the filter to use 60 points or higher before classifying it as spam. Is that analogous to choosing a higher or lower alpha level for a hypothesis test. Explain in terms of the hypotheses above.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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