On any given day, a student is either healthy or ill. Of the students who are healthy today, 95 percent will be healthy tomorrow. Of the students who are ill today, 55 percent will be ill tomorrow. Let ro (respectively yo) be the proportion of students who are healthy (respectively ill) on Monday. Let x, (resp. Yn) be the proportion of students who are healthy (resp. ill) after n days. You may define a matrix A: (:) (::)(:)-) Example of a 2 x 2 matrix A = such that a. In+1 Yn Yn+1 for all n 20. Suppose that 20 percent of students are ill on Monday. What percentage of students will still be ill on Tuesday? on Wednesday? in n days? Your teacher thinks about the attandance to class so he wants to know. From the given information above, you determine the ill student percentage is in the long term (as n gets very large). Note : The answer must be an integer and its value must be between 0 and 100.
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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