8 Spectacled weavers are birds that use grass to weave nests that look like hanging baskets. The male bird weaves a nest and then invites the female to inspect the nest. If no female accepts the nest, the male will build another nest; the male continues to build new nests until a female accepts. 200 male birds were observed, and X, the number of nests that were rejected by the females before a nest was accepted, was recorded for each male bird. The results are given in the first two columns of Table 1. Table 1: Number of rejected nests of 200 male weaver birds No. rejected (x) No. male birds (fi) Pi 128 0.625 1 44 0.234 12 0.0879 3 12 0.03296 4 4 0.02014 Total 200 (a) Write down a possible distribution for these data, giving reasons for your choice. (b) Calculate the sample mean and standard deviation for these data and use these answers to estimate the parameter(s) for the distribution. (c) Write down the formula to calculate P(X = 2) = P2 = 0.0879 (4 dp). Show clearly how to use the answer to (b) to calculate the value given here.
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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