Merge pull request #13 from virtual-labs/dev

Updated the formatting of various pages

Author: shraddha

experiment/procedure.md

@@ -1,21 +1,56 @@
-**Stage 1:**
+**Stage 1: Understanding Random Variables and Distributions**
 
-  1. Set the default parameters and click the generate button; Observe the dataset for multiple instances of samples.
+  1. Select a distribution type (Uniform, Normal, or Exponential) from the dropdown menu.
 
-  2. Click the estimate button to compute the mean and covariance of the generated samples; Observe the mismatch between the two. Repeat the process for multiple sets of samples generated from the same distribution and observe the variations in the estimate.
+  2. Adjust the distribution parameters using the sliders:
+     - For Uniform: Set the minimum and maximum values
+     - For Normal: Set the mean and standard deviation
+     - For Exponential: Set the rate parameter
 
-**Stage 2:**
+  3. Set the number of points (100-1000) using the slider.
 
-  1. Repeat the above procedure for the different values for the number of generated samples.
+  4. Click "Generate Data" to create a new dataset.
 
-  2. Plot a graph between the average error, and number of samples
+  5. Observe the generated points on the plot and the basic statistics (mean and standard deviation) in the information panel.
 
-  3. Note down your inferences regarding the graph.
+  6. Repeat steps 1-5 with different parameter values to understand how they affect the distribution.
 
-**Stage 3:**
+**Stage 2: Analyzing Sample Size Effects**
 
-  1. Generate your own dataset by clicking on the plot area. Note that the distribution need not be similar to a normal density.
+  1. Choose a distribution type and set its parameters.
 
-  2. Estimate the mean and covarance matrices.
+  2. Generate datasets with different sample sizes (e.g., 100, 300, 500, 700, 1000).
 
-  3. Note down your inferences regarding the error committed if you assume the distribution to be normal.
+  3. For each sample size:
+     - Generate multiple datasets
+     - Record the mean and standard deviation
+     - Note how these statistics vary with sample size
+
+  4. Compare the observed statistics with the theoretical values:
+     - For Uniform: mean = (min + max)/2, variance = (max - min)²/12
+     - For Normal: mean = μ, variance = σ²
+     - For Exponential: mean = 1/λ, variance = 1/λ²
+
+  5. Draw conclusions about how sample size affects the accuracy of statistical estimates.
+
+**Stage 3: Interactive Data Generation and Analysis**
+
+  1. Use the "Animate" button to see how the points are generated in real-time.
+
+  2. Try different combinations of:
+     - Distribution types
+     - Parameter values
+     - Sample sizes
+
+  3. Observe how the shape of the distribution changes with different parameters.
+
+  4. Compare the theoretical distribution shape with the actual generated points.
+
+  5. Note how the basic statistics (mean and standard deviation) help characterize the distribution.
+
+**Learning Objectives:**
+- Understand different types of random variables and their distributions
+- Learn how parameters affect the shape and characteristics of distributions
+- Observe the relationship between sample size and statistical accuracy
+- Develop intuition about probability distributions through interactive visualization
+- Understand basic statistical measures (mean and standard deviation) in the context of different distributions