I. For any uniform probability distribution, the mean and standard deviation can be computed by knowing the maximum and minimum values of the random variable. a) true
b) false
ii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
a) true
b) false
iii. The uniform probability distribution's shape is a rectangle
a) true
b) false

Answer: I. True

II. True

III. True

Step-by-step explanation:

Uniform probability distributions, this are probability distributions which have equally likely outcomes. There are two known types of uniform distributions:

1. discrete

2. continuous.

In the first type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous this means they are usually infinite.

Final answer:

In a uniform probability distribution, both the mean and standard deviation can be derived from the minimum and maximum values, P(x) remains constant, and the shape of the distribution is rectangular. All statements are true.

Explanation:

The answer to your questions:
i. For any uniform probability distribution, the mean and standard deviation can indeed be computed by knowing the maximum and minimum values of the random variable. So, this is true. The mean is the average of the maximum and minimum, and the standard deviation can be calculated from the range (max-min).

ii. In a uniform probability distribution, P(x) is indeed constant between the distribution's minimum and maximum values. This means that every value has the same likelihood of occurring, which is what makes it 'uniform'. So, this is true.

iii. The uniform probability distribution's shape is indeed a rectangle. This is because all outcomes are equally likely, resulting in a graph that is flat, or rectangular-shaped. Hence, this is also true.

Learn more about Uniform Probability Distribution here:

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