By theoretical distribution we mean a frequency distribution, which is obtained in relation to a random variable by some mathematical model. The examples of such a distribution are : (i) Binomial distribution, (ii) Poisson distribution, (iii) Normal distribution or Expected Frequency distributions of a random variable, which are built up one these distributions, a random exponent is theoretically consideration. For these distribution, a random exponent is theoretically assumed to serve as a model, and the probabilities are given by a function of the random variable, called probability function. For instance, if we toss a fair coin, random variable, called probability function. For instance, if we toss a fair coin, we know that the probability of getting a head is ½. If we toss it 50 times, the number of heads likely to come up is 25. This is the theoretical, or expected frequency of the heads. But in actual tossing, we may get 25,30 or 35 heads which would be called the observed frequency. Thus, the observed frequency and the expected frequency may equal with, or may differ from each other due to some bias, or fluctuation in sampling. If we toss 5 coins for 150 times, we can have a set of observed frequencies by conduction an experiment. We can, also, find its expected frequencies by applying the model, 150 (½+ ½)5, or any other mathematical model based on some definite probability law according to which the value of the random variable may be distributed in the population.
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