统计与概率
已验证计算器，公式透明
Discrete Uniform Distribution Calculator.
Calculates the probability of a specific outcome or a range of outcomes for a discrete uniform distribution, where each outcome is equally likely.
您的输入
工作原理
- 1
Enter the minimum value a and maximum value b of the distribution.
- 2
Enter the value x for which you want the probability.
- 3
Check if x is between a and b inclusive.
- 4
If yes, divide 1 by the number of outcomes (b - a + 1); otherwise the probability is 0.
(x >= a && x <= b) ? 1/(b - a + 1) : 0常见问题
What is a discrete uniform distribution?
It's a distribution where each of the finite number of outcomes has an equal probability. For example, a fair die has outcomes 1 to 6 each with probability 1/6.
How do I calculate the probability of a range?
For a range from x1 to x2, the probability is (x2 - x1 + 1) / (b - a + 1) if the range is within [a, b]. This calculator gives the probability for a single value.
What if x is outside the range?
The probability is 0 because the outcome is impossible.
工作原理
Calculates the probability of a specific outcome or a range of outcomes for a discrete uniform distribution, where each outcome is equally likely.
- Enter the minimum value a and maximum value b of the distribution.
- Enter the value x for which you want the probability.
- Check if x is between a and b inclusive.
- If yes, divide 1 by the number of outcomes (b - a + 1); otherwise the probability is 0.
公式
此计算器背后的数学公式，供您核对结果。
Probability mass function
Each outcome in the range from a to b is equally likely, so the probability of any specific value is one divided by the total number of outcomes.
Example:
Input: a = 1, b = 6, x = 3
Calculation: 1 / (6 - 1 + 1) = 1/6
Result: ≈ 0.1667
实际应用场景
此计算在日常生活中的应用。
Fair dice rolls
Determine the probability of rolling a specific number on a fair die.
Example: P(roll a 4) = 1/6 ≈ 0.1667
Random selection
When picking a random integer from a set, find the chance of picking a particular one.
Example: From numbers 1 to 10, P(5) = 0.1
Quality control
If defects are uniformly distributed across a batch, estimate the probability of a specific defect location.
Example: Batch of 100 items, P(item 50 is defective) = 1/100 = 0.01
提示与常见错误
Tips
- Ensure a ≤ b; otherwise the distribution is invalid.
- The number of outcomes is b - a + 1, so the probability is 1 divided by that count.
- For ranges, multiply the single-value probability by the number of values in the range.
- Use this calculator for discrete integer outcomes only, not continuous values.
Common Mistakes to Avoid
- Forgetting that the range is inclusive, so the count is b - a + 1, not b - a.
- Using a probability greater than 1 when the range is small.
- Assuming x must be an integer; it can be any number, but if it's not an integer, the probability is 0.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.