A$.$ Write a for loop that computes the product of all odd numbers from $1$ to $51.$ At the end of the loop, your code should produce the final message "The product of all odd numbers between $1$ and $51$ is $x",$ where $x$ is your answer.

B$.$ Write a for loop that counts the number of negative numbers in a list of $5000$ random numbers between $-1$ and $1,$ generated by the runif command. Use an if$/$else command in the loop to count $"+1"$ when number is negative and does not count if the number is nonnegative.

Your code for this part should end with the text "The number of negative numbers is $Z",$ where $Z$ is the number of negative numbers.

C$.$ Repeat the previous step, except compute the number of negative numbers in $2000$ randomly generated vectors, each of which contains $5000$

numbers. As part of this process your code should create a vector with $2000$ elements, each of which is the # of negative numbers in one of

the randomly generated $5000-$element vectors. Use the mean command to find the average number of negative numbers in the $2000$ vectors.

Your code should end with the sentence "The average number of negative numbers in the $2000$ random vectors is $Z",$ where $Z$ is the average. You will need a for loop outside of the for loop

from the previous step. This is called a nested for loop. What number is closest to your average? Is it what you expected?

D$.R$ allows for a much faster way to count the number of elements ina vector that satisfy a certain condition. If myvector is your $5000$

element vector of random numbers, the command sum $($myvector $<mn\; id="EditorElement\_325312">0</mn><mtext\; id="EditorElement\_324906"></mtext><mi\; id="EditorElement\_324907">)</mi>$ will count the number of elements less than $0.$ Use this fact to modify your code from the previous step so that you only use ONE for loop. But this time, generate $10000$ random vectors, each with $10000$ elements. Assign the name numnegs to the $10000$ element vector that contains the number of negative numbers found in each of the $10000$ randomly generated vectors of $10000$ numbers between $-1$ and $1.$