मुफ्त समान वितरण कैलकुलेटर
समान (यूनिफॉर्म) वितरण की प्रायिकता और माध्य निकालें। सीमाएं दर्ज करें।
PDF f(x)
0.10000000
PDF f(x) vs Lower Bound (a)
सूत्र
How to Calculate Uniform Distribution Properties
Formulas
PDF: f(x) = 1 / (b - a) for a <= x <= b
CDF: P(X <= x) = (x - a) / (b - a)
The continuous uniform distribution assigns equal probability density to all values in the interval [a, b]. The probability of falling in any sub-interval depends only on the sub-interval's length relative to the total range. The mean is the midpoint (a+b)/2.
हल किया गया उदाहरण
A bus arrives uniformly between 0 and 10 minutes. What is P(arrival <= 7 min)?
- 01PDF = 1 / (10 - 0) = 0.1
- 02CDF = (7 - 0) / (10 - 0) = 0.7
- 03P(X <= 7) = 70%
- 04Mean = (0 + 10) / 2 = 5
- 05Variance = (10 - 0)^2 / 12 = 100/12 ≈ 8.3333
अक्सर पूछे जाने वाले प्रश्न
Why is the PDF constant?
Because every value in [a,b] is equally likely. The height 1/(b-a) ensures the total area under the curve equals 1, as required for a valid probability distribution.
How do I find P(c < X < d) for a uniform distribution?
P(c < X < d) = (d - c) / (b - a), as long as a <= c < d <= b. The probability depends only on the length of the interval relative to the total range.
What is the discrete uniform distribution?
The discrete version assigns equal probability 1/n to each of n possible outcomes. For example, a fair die has a discrete uniform distribution on {1, 2, 3, 4, 5, 6} with P(x) = 1/6.
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