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The modes of a probability density function might be defined as the (countable) set of points in the domain of the function for which the function achieves local maxima. Since the probability density function for the uniform distribution is constant by definition it has no local maxima, hence no modes. Hence, it cannot be bimodal.
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What if there a two modal class?
The distribution is bimodal. That is all there is to it.
Is considerably skewed distribution the same as bimodal distribution?
No. A distribution may be non-skewed and bimodal or skewed and bimodal. Bimodal means that the distribution has two modes, or two local maxima on the curve. Visually, one can see two peaks on the distribution curve. Mixture problems (combination of two random variables with different modes) can produce bimodal curves. See: http://en.wikipedia.org/wiki/Bimodal_distribution A distribution is skewed when the mean and median are different values. A distribution is negatively skewed when the mean is less than the median and positively skewed if the mean is greater than the median. See: http://en.wikipedia.org/wiki/Skewness
Is the uniform probability distribution is symmetric about the mode?
Yes, the uniform probability distribution is symmetric about the mode. Draw the sketch of the uniform probability distribution. If we say that the distribution is uniform, then we obtain the same constant for the continuous variable. * * * * * The uniform probability distribution is one in which the probability is the same throughout its domain, as stated above. By definition, then, there can be no value (or sub-domain) for which the probability is greater than elsewhere. In other words, a uniform probability distribution has no mode. The mode does not exist. The distribution cannot, therefore, be symmetric about something that does not exist.
What is the variance of the uniform distribution function?
the variance of the uniform distribution function is 1/12(square of(b-a)) and the mean is 1/2(a+b).
Can the Empirical Rule of probability be applied to the uniform probability distribution?
Yes, except that if you know that the distribution is uniform there is little point in using the empirical rule.
