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You’re drawing from a random variable that is normally distributed \(X \sim \mathcal{N}(0,1)\)  once per day.

What is the expected number of days that it takes to draw a value that’s higher that 2?

How many draws from a standard normal distribution would you expect to take to obtain a value higher than 2?

How many draws from a standard normal distribution would you expect to take to obtain a value higher than 2?

Drawing Random Variable

Imagine you have been given an array of integers, and a query number <code>k</code>. Your task is to write a function that finds all the triplets in the array that sum up to the query number <code>k</code>.

Let’s illustrate this with some examples:

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>nums = [1, 2, 3, 4, 5]
k = 6
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>count_triplets(nums, k) -&gt; 1
</code></pre>

In this case, there is only one triplet that sums up to 6: (1, 2, 3).

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>nums = [10, 10, 20, 30, 40]
k = 60
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>count_triplets(nums, k) -&gt; 3
</code></pre>

In this case, there are three triplets that sum up to 60: (10, 10, 40), (10, 20, 30), and (10, 20, 30).
The value 10 can be retrieved as <code>nums[0]</code> or <code>nums[1]</code>, therefore resulting in two triplets with the same value.

Write a function that returns the number of triplets in the array that sum to `k`.

Triplet Counting

“Suppose you are given a matrix of integers. Your task is to write a function that returns the sum of the elements in the matrix.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>matrix_sum(matrix) -&gt; 45
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>matrix_sum(matrix) -&gt; -45
</code></pre>

The function should be able to handle both positive and negative integers and should return the sum as an integer.

The task is to find the sum of all elements in a given matrix of integers.

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