A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. P(x) D 0.093 1 0.327 0.423 3 0.157 Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable x's number values are not associated with probabilities. C. No, the sum of all the probabilities is not equal to 1. D. No, the random variable x is categorical instead of numerical. E. No, not every probability is between 0 and 1 inclusive.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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