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. ii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
iii. The uniform probability distribution's shape is a rectangle.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

For a uniform probability distribution, the mean and standard deviation can be calculated using the following formulas:

Mean = (Maximum + Minimum) / 2

Standard Deviation = (Maximum - Minimum) / √12

Therefore, statement (i) is correct.

In a uniform probability distribution, the probability density function is constant between the minimum and maximum values. This means that all outcomes within the range have an equal probability of occurring. Hence, statement (ii) is also correct.

Finally, the shape of a uniform probability distribution is a rectangle, since the height (probability) is constant between the two endpoints. Therefore, statement (iii) is also correct.

Hence, the correct choice is (A).

I for Any Uniform Probability Distribution, the Mean and Standard