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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.
The shape of any uniform probability distribution is?
Rectangular
Does this means that all symmetric distribution are normal Explain?
Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.
