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Which Statements Below Accurately Characterize a Uniform Distribution. Select All That Apply.

A uniform distribution, also known as a rectangular distribution, is a probability distribution in which all outcomes are equally likely. It is characterized by a constant probability density function, meaning that the probability of any particular outcome within a given range is the same. Below are some statements that accurately describe a uniform distribution:

1. All outcomes have the same probability: In a uniform distribution, every outcome has an equal chance of occurring. This means that the probability of obtaining any specific value is constant.

2. The probability density function is constant: The probability density function (PDF) of a uniform distribution remains the same throughout the entire range. This indicates that the distribution is flat and uniform.

3. The range of possible outcomes is known: In a uniform distribution, the range of possible outcomes is well-defined. This range can be from a minimum value (a) to a maximum value (b).

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4. The mean and median are equal: The mean and median of a uniform distribution are always equal, as the distribution is symmetrical.

5. The variance is calculated using a specific formula: The variance of a uniform distribution can be calculated using the formula ((b-a)^2)/12, where ‘a’ is the minimum value and ‘b’ is the maximum value.

Q1. What is the purpose of a uniform distribution?
A1. A uniform distribution is often used in probability and statistics to model situations where all outcomes are equally likely.

Q2. Can a uniform distribution have any shape?
A2. No, a uniform distribution is always flat and rectangular in shape.

Q3. Are there any real-life examples of a uniform distribution?
A3. Yes, examples include the rolling of a fair die, the selection of a random number between two values, or the distribution of birth dates in a large population.

Q4. Is a uniform distribution symmetric?
A4. Yes, a uniform distribution is symmetric as the mean and median are equal.

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Q5. What is the difference between a uniform distribution and a normal distribution?
A5. A uniform distribution has a constant probability density function, while a normal distribution has a bell-shaped curve with higher probabilities at the mean.

Q6. Can a uniform distribution be skewed?
A6. No, a uniform distribution cannot be skewed as it is symmetrical.

Q7. How is the variance calculated in a uniform distribution?
A7. The variance of a uniform distribution can be calculated using the formula ((b-a)^2)/12, where ‘a’ is the minimum value and ‘b’ is the maximum value.