Uniform Distribution

The distribution of points obtained in a single throw of an unbiased die is an example of uniform distribution. This is because each of the six faces of the die has an equal probability of appearing, i.e., 1/6. Therefore, the probability of obtaining any particular number between 1 and 6 is the same, and the distribution of points is uniform.

Definition of Uniform Distribution

Uniform distribution is a probability distribution where every possible outcome has an equal chance of occurring. In other words, the probability of any event is the same, and the distribution is flat or uniform. A uniform distribution is often used to model situations where every outcome is equally likely.

Characteristics of Uniform Distribution

Some of the characteristics of the uniform distribution are:

1. The probability density function (PDF) is constant over the range of possible values.

2. The mean and variance of the distribution can be easily calculated.

3. The distribution is symmetric.

4. The distribution is defined by its minimum and maximum values.

Conclusion

In conclusion, the distribution of points obtained in a single throw of an unbiased die follows a uniform distribution. This is because each of the six faces of the die has an equal probability of appearing, and the distribution is flat or uniform. The characteristics of the uniform distribution include a constant PDF, easy calculation of mean and variance, symmetry, and definition by minimum and maximum values.

It's uniform distribution because the probability to get any number (from 1 to 6)obtained in a single throw of an unbiased die is the same(i.e., P=1/6).