Which of the following is not a characteristic of a uniform distribution?a.All outcomes are equally likely.b.The probability density function is constant within a given interval.c.The mean and standard deviation are equal.d.The distribution is symmetric.
Question
Which of the following is not a characteristic of a uniform distribution?a.All outcomes are equally likely.b.The probability density function is constant within a given interval.c.The mean and standard deviation are equal.d.The distribution is symmetric.
Solution
The characteristic that is not a feature of a uniform distribution is: c. The mean and standard deviation are equal.
Here's why:
a. All outcomes are equally likely: This is true for a uniform distribution. In a uniform distribution, all outcomes in a specified range are equally likely to occur.
b. The probability density function is constant within a given interval: This is also true for a uniform distribution. The probability density function of a uniform distribution is constant, which means that the probability of any given outcome occurring is the same across the entire distribution.
c. The mean and standard deviation are equal: This is not true for a uniform distribution. In a uniform distribution, the mean is the midpoint of the range of possible outcomes, while the standard deviation depends on the range of the distribution. They are not necessarily equal.
d. The distribution is symmetric: This is true for a uniform distribution. A uniform distribution is symmetric, meaning that the distribution is the same on both sides of the mean.
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