Data Loading and Preliminary Analysis

Load the "penguins.csv$"$ dataset into a DataFrame.

Display the first few rows of the dataset and summarize its structure, including the number of rows$/$columns and data types.

Data Cleaning and Preprocessing

Check for and handle missing values in the dataset.

Exploratory Data Analysis

Create visualizations:

Histograms or box plots for the distribution of numerical features.

Bar charts for categorical attributes.

Pair plots or scatter plots to explore relationships between features$\mathrm{.}4.$

$4.$ Advanced Statistical Analysis

Compute the Multivariate Mean Vector: Calculate the mean for each attribute in the dataset.

Compute the Sample Covariance Matrix $($Inner Product$)$: Use the inner product between the columns of the centered data matrix$($Numerical Attributes only$).$

Compute the Sample Covariance Matrix $($Outer Product$)$: Use the outer product between the centered data points$($Numerical Attributes only$).$

Compute the Correlation Between Two Attributes$($bill$\_$length$\_$mm$,$ bill$\_$depth$\_$mm$)$

Compute the correlation between the two attributes$($bill$\_$length$\_$mm$,$ bill$\_$depth$\_$mm$)$ by calculating the cosine of the angle between the centered attribute vectors. Include a scatter plot of these two attributes.

Compute the Covariance matrix of the three categorical attributes$($species$,$ island, and sex$).$

Probability Density Function: Assuming the first numerical attribute is normally distributed, plot its probability density function.

Empirical CDFs: Plot the Empirical Cumulative Distribution Functions $($CDFs$)$ of attributes bill$\_$length$\_$mm$,$ bill$\_$depth$\_$mm$,$ and body$\_$mass$\_$g$..$

Variance Analysis: Identify the numerical attribute with the largest variance and the one with the smallest variance. Print these values.

Covariance Analysis: Determine which pair of attributes has the largest and smallest covariance. Print these values.