Need to calculate Shannon entropy

It is not at all clear what you are talking about.
You have four different definitions of X.
Nothing here sounds anything like entropy.

Are you taking a course or reading a textbook?  If so, what is the title?
And maybe a little more information on the calculation and formula that you mentioned.

>> using the formula
I don't see the formula you are using. Post it. Where did you get this formula?

>> but I'm not sure if its right.
What are you not sure about - the formula or your computation when you use the formula? Clarify and post whatever you have.

Yes sorry its shannon entropy formula
A answer is 1.59
B answer is 2
C, D I don't know how to calculate

Thanks for the additional information.

Information Entropy is very different from Thermodynamic Entropy.

The formula you need is   Log_2(X)  which is the logarithm to the base 2.

You can calculate it using either   log(x)/log(2)   or   ln(X)/ln(2)    where log(X) is base 10 and ln(X) is base e

log(1000)/log(2) = 9.966    and log(1024)/log(2) = 10

Note: The common sense definition of Shannon Entropy is the number of bits required to encode a particular variable.  You always have to round up.  So (a) and (b) are the same, and so are (c) and (d).

Could you show us how you calculated the results that you said are correct?

Is this question resolved?

Do you see how to simplify the formula when the N  values of  X  are uniformly distributed?  That means that all the p_i = 1/ N

Here are some log formulas that will help you.

Log Rules:

1) log(mn) = log(m) + log(n)

2) log(m/n) = log(m) – log(n)

3) log(m^n) = n · log(m)

Select allOpen in new window

https://www.purplemath.com/modules/logrules.htm

For the first one its so easy first two but I cant do it for the 3rd and forth
https://ibb.co/pz4gQ9x

>> but I cant do it for the 3rd and forth
Post what you have done and tell us where you are having trouble.

Note in (b), you have three identical terms.

In (c) and (d), you will have 1000 and 1024 identical terms.
You should be able to simplify these expressions to get just a -log(1/N) term.

Apply the log formula that are posted above., and post your work.