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It is a probability distribution where when all of the values of a random variable occur with equal probability.
Say X is the random variable, such as what number shows up when we roll a die.
There are 6 possible outcomes, each with a 1/6 probability of showing up.
If we create a probability distribution where X= 1,2,3,4,5, or 6, we note
P(X=k)=1/k where k is any number between 1 and 6 in this case.
The graph will be a rectangle.
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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.
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
Is the uniform probability distribution is symmetric about the mean and median?
yes
The probability density function for a uniform distribution ranging between 2 and 6 is?
4
