Prompt
Create an image of a graph showing a Student's t-distribution curve with varying degrees of freedom, set against a backdrop of statistical formulas and notations, with a subtle pattern of data plots and charts. The curve should be plotted in a realistic style, with a muted color palette and clear labels, illustrating how the distribution changes as the degrees of freedom increase, ultimately approaching a Normal distribution. The image should convey a sense of mathematical precision and statistical analysis.
