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How do you guess the lottery numbers?
pick six random numbers
What is the formula of a mean?
Obtain the arithmetic mean of a batch of numbers by adding them up and dividing by their count. For example, the arithmetic mean of 3, 5, and 10 equals (3 + 5 + 10)/ 3 = 6. There are other kinds of means, such as geometric and harmonic, but usually when the type of mean is not specified the arithmetic mean is intended. For completeness I will also provide an answer from probability theory. The mean of a random variable is its expectation, which is defined to be its integral. If the random variable has a distribution f(x)dx, its mean equals the integral of x*f(x)dx over all real numbers. This is related to the first definition of arithmetic mean. A batch of numbers gives rise to a random variable supported at those numbers, where the probability of each number is proportional to the number of times it occurs in the batch. (This is the empirical distribution function of the batch.) The arithmetic mean of the batch equals the expectation of that random variable.
What is the signifance of the mean of a probability distribution?
It is the average of all the numbers in the distribution. If you chose a random data point of the distribution, there would be a 50% chance that it is above the mean, and a 50% chance that it is below the mean.
How is a random sample selected?
There are a few ways to do this, but one of the most common ways is by giving each of your subjects a number. If there are 100 of them, number them 001-100. If there are 1000, number them 0001-1000 and so on. Then, randomly choose numbers for each group using random number generator.
Why is it important to ensure that an experimental sample is totally random?
To ensure that the results produced from your sample are fair and true. For example, if you had to pick 10 random numbers between 1 and 6, you could just say numbers that come into your head, but that wouldn't be random because you're choosing the numbers. A more random and fair way would be to roll a die 10 times and use those numbers, because you are in no way picking the numbers.
