Your are working in an AI tech consulting firm, mighty.ai

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$$Recently a new client YogaSoda approach to

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$$your company for helping with its product inventory problem. YogaSoda produces and sells its soft drink product line via millions of its own vending machines across the US

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$$Efficiently managing the inventory of each vendor machine based on customer selections poses a daunting challenge..

The project manager Bob Boss has conducted a detailed study with YogaSoda that leads to the following key findings:

A YogaSoda vending machine needs to manage its soda inventory efficiently based on customer selections.

Customers make choices without directly indicating their preferences.

The vending machine uses a sensor to detect whether a regular or diet soda is selected.and decided to design and deploy an AI

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based inventory management software on each YogaSoda vendor machine to help it make intelligent decision in dynamic and uncertain environments.

Based on these findings, Boss Bob has come up with the following key product specification:

The AI software app shall estimate the most likely sequence of customer preferences, enabling the management of inventory for restocking and ensuring customer satisfaction.

It shall use the HMM with the Viterbi algorithm that allows the vending machine to decode the most likely sequence of customer choices.

This information is crucial for optimizing inventory levels, predicting future demand, and maintaining a balanced stock of regular and diet sodas.

The HMM assists in making informed decisions, especially when there is uncertainty about customer preferences over time.Now Bob Boss asks you to complete the following assignments that consists of two parts: minds$-$on and hands$-$on$.$

Problem #$1$: the Minds$-$on Part

$1.$ What are the hidden states?

$2.$ What are the observations?

$3.$ What are the HMM parameters $($Initial State Probability, Transition Matrix, and Emission Matrix, respectively$)?$

Problem #$2$:

You need to implement the AI app in Python that has the following functions:

$1.$ Simulate customer choices and observations in the vending machine scenario

$2.$ Apply the Viterbi algorithm to decode the most likely sequence of hidden states