Let me extract and analyze the content of the image for solving your mathematical problem. One moment Image import pytesseract

Load the image from the file path

image_path = "/mnt/data/1732909797889ptojxawz.jpg" image = Image.open(image_path)

Use OCR to extract text from the image

extracted_text = pytesserThe text extracted from the image is distortedFrom the handwritten text in your image, it appears that you're trying to show that $E[f(X)] = f(E[X])$ under certain conditions. This is likely related to expectation properties or a specific mathematical justification for the equality involving $X$, $f(X)$, and $E[X]$.

To assist further, please clarify or verify the problem statement if possible (e.g., if specific conditions are given). Meanwhile, here are steps for approaching problems like this:

General Idea:

1. The equation $E[f(X)] = f(E[X])$ is not true in general unless $f$ is a linear function. That is, $f(x) = ax + b$, since expectation generally does not commute with non-linear functions.
2. If you're working with special cases (e.g., $f(x) = ax$ or other constraints), proving this equality depends on properties of $f(x)$ and $X$.

Let me know if you'd like further clarification, or feel free to provide a clearer photo