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Morgan Stanley Interview Questions

A/B Testing

Algorithms

Analytics

Machine Learning

Probability

Product Metrics

Python

Statistics

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Write a Python function called <code>max_profit</code> that takes a list of integers, where the i-th integer represents the price of a given stock on day i, and returns the maximum profit you can achieve by buying and selling the stock.

You may complete, at most, two complete buy/sell transactions to maximize profits on a stock.

Input:

<pre tabindex="0" class="chroma"><code>prices = [3, 3, 5, 0, 0, 3, 1, 4]
</code></pre>

Output:
6

Explanation:

Buy on day 4 (price = 0) and sell on day 6 (price = 3): profit = 3 - 0 = 3.
Then buy again on day 7 (price = 1) and sell on day 8 (price = 4): profit = 4 - 1 = 3.
Total profit: 3 + 3 = 6.

Maximum Profit

Let’s say that your company is running a standard control and variant AB test on a feature to increase conversion rates on the landing page. The PM checks the results and finds a .04 p-value.

How would you assess the validity of the result?

Experiment Validity

Let’s say we have a table with an <code>id</code> and <code>name</code> fields. The table holds over 100 million rows and we want to sample a random row in the table without throttling the database.

Write a query to randomly sample a row from this table.

Input:

<code>big_table</code> table

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>

Write a query to randomly sample a row from a big table.

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