概率分布 - 函数、公式、表格
理解概率分布及其函数、公式和表格
Interactive Probability Distribution Visualization
Welcome to the Probability Distribution Explorer
This interactive visualization helps you understand different probability distributions, their properties, and how parameters affect their shape. Explore discrete and continuous distributions with real-time parameter adjustments.
What you can explore:
- Discrete Distributions: Binomial, Poisson, Geometric (PMF)
- Continuous Distributions: Normal, Uniform, Exponential (PDF)
- Properties: Mean, variance, standard deviation
- Cumulative Distribution: CDF visualization
How to Use This Visualization
Interactive Features:
- • Select Distribution - Choose from 6 different distributions
- • Adjust Parameters - Change distribution parameters with sliders
- • Toggle CDF - Show/hide cumulative distribution function
- • Explore Values - See probability at specific x values
What You'll See:
- • PMF/PDF Graph (green) - Probability mass/density function
- • CDF Graph (blue, dashed) - Cumulative distribution function
- • Point Marker (orange) - Selected x value
- • Properties Panel - Mean, variance, standard deviation
Number of successes in n independent trials
Probability at x = 0
PMF
0.0000
P(X = x)
CDF
0.0000
P(X ≤ x)
Distribution Properties
Mean (μ)
NaN
Expected value
Variance (σ²)
NaN
Measure of spread
Std Dev (σ)
NaN
Square root of variance
Key Concepts
PMF (Discrete): Probability Mass Function - P(X = x) for discrete random variables
PDF (Continuous): Probability Density Function - f(x) for continuous random variables
CDF: Cumulative Distribution Function - P(X ≤ x) or F(x)
Mean: Expected value, center of the distribution
Distribution Applications
Binomial: Coin flips, success/failure experiments
Poisson: Rare events, arrivals, counts
Geometric: Waiting times, first success
Normal: Natural phenomena, measurement errors
Uniform: Equal probability, random selection
Exponential: Time between events, decay processes
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