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Uniform Discrete Distribution

Probability Calculator

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QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Calculator > Uniform Discrete

The Uniform Discrete distribution is a discrete probability distribution. Each of the values are equally likely. The uniform discrete has two parameters; a, the Lower Bound and b, the Upper Bound. For purpose of simplification, n, or the number of possible values, is calculated from a and b. See the pdf formula below.

UniformDiscrete

Using the Calculator

Step 1

Enter the Lower, Upper, and X value (optional).

Step 2

Quantum XL will plot the probability for every X from the lower to the upper.

If X was supplied:

  • The bar corresponding to X will be red.

  • At the bottom of the report, Quantum XL will provide the numeric results for X being less than, less than or equal to, greater than, greater than or equal to, and equal to.

Understanding the Results

die

A fair six-sided die (one dice) generates uniform discrete random numbers from 1 to 6. For the analysis below, the lower = 1 (smallest possible die roll) and the upper = 6 (largest possible die roll). If you were interested in the probability of rolling a 5, enter 5 for "X Value".

Since each number, 1 through 6, is equally likely the bars are all the same height.

  • P(X=5) indicates that the probability of rolling a 5 on any roll is .16667 which is one sixth.

  • P(X<5) indicates that the probability of rolling a number less than 5 on any roll is .6667 which is 4/6.

  • P(X<=5) indicates that the probability of rolling 5 or less on any roll is .8333.

  • P(X>5) indicates that the probability of rolling a number greater than 5 on any roll is .16667.

  • P(X>=5) indicates that the probability of rolling a 5 or larger on any roll is .3333.

UniDiscExample

See Also