The following table shows the marks obtained by a class at the St. Vincent and the Grenadines community college in the probability and statistics course, GED 103. Both tests were marked out of 60. Final exam mark 49 44 20 32 25 35 40 17 31 28 Mid-semester mark Student 35 44 42 37 10 43 50 14 40 10 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Let X represent the marks obtained on the mi bemester exam and Y represent the mark obtained on the final exam. 11 39 30 34 41 22 46 32 39 34 40 16 30 40 43 28 35 39 27 26 34 34 37 27 34 49 50 47 31 37 41 51 45 38 42 36 36 41 30 46 35 41 a In which exam did the students did better overall? Justify your answer ai Calculate the correlation coefficient using the formula given. ü. What conclusions cam you make about the relationship between performances on the two eams?
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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