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Let’s say that you’re a data scientist at Robinhood. 

How do we measure the launch of Robinhood’s fractional shares program?

Let’s say you are a data scientist at Robinhood.

Robinhood is introducing a program to allow users to buy fractional shares of publically listed companies.

Focusing in on the activity of new users, which of the following metrics would be the LEAST important to keep track of in determining if the program added value to Robinhood’s platform for new users?

Let's say you are a data scientist at Robinhood. 



Robinhood is introducing a program to allow users to buy fractional shares of publically listed companies.



Focusing in on the activity of new users, which of the following metrics would be the LEAST important to keep track of in determining if the program added value to Robinhood's platform for new users?

Fractional Shares Metrics

Fractional Shares

Given two independent standard normal random variables $X$ and $Y$, what’s the probability that $2X > Y$?

If $X$ and $Y$ both follow a standard normal distribution ($\mathcal{N}(0,1)$), what distribution does $2X - Y$ follow?

If $X$ and $Y$ both follow a standard normal distribution ($\mathcal{N}(0,1)$), what distribution does $2X - Y$ follow?

2X - Y

If you multiply a random variable by a negative number, say -a, what happens to its variance?

If you multiply a random variable by a negative number, say -a, what happens to its variance?

Multiplying Random Variables

Let

\[f(x,y)=5^x\cdot 3^y\]

Given an interval $[L,R]$ and some integer $N$. Write a function, <code>get_possible_values</code>, that returns all positive integer pairs $(x,y)$ such that $f(x,y)\in[L,R]$ and $x,y\lt N$.

Example:

Input:

<pre tabindex="0" class="chroma"><code>L = 0
R = 1
N = 50
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>get_possible_values(L, R, N) -&gt; [[0,0]]
</code></pre>

Since $f(0,0)=1\in [0,1]$

Find all integer pairs that when plugged in into a function, their values within some interval

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