Here are my answers to the second chapter of Computer Networks by Andrew Tanenbaum 4th edition with ISBN 0130661023.

Problem №3:
Television channels are 6 MHz wide. How many bits/sec can be sent if four-level digital signals are used? Assume a noiseless channel.

Using Henry Nyquist’s theorem we have 2Nlog2(V) where N is 6MHz, and V is 4
gives us 24mbit/s

Problem №4:
If a binary signal is sent over a 3-kHz channel whose signal-to-noise ratio is 20 dB, what is the maximum achievable data rate?

Using the formula Hlog2(1+S/N), and from the chapter we know that 20dB is 100S/N, we can calculate that 3000* 6.65821148 = 19 974.6344 bits per second

Problem №5:
What signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line?

Since first grade we know that T1 is about 1.544 million bits per second theoretical speed :)
So using the same formula as above we have:
1544000 = 50000*log2(1+S/N)
log2(1+S/N) = 30.88
1+S/N = 1976087930
S/N = 1976087929
10log10(1976087929) = approx 92.95806263 dB

Problem №8:
It is desired to send a sequence of computer screen images over an optical fiber. The screen is 480 x 640 pixels, each pixel being 24 bits. There are 60 screen images per second. How much bandwidth is needed, and how many microns of wavelength are needed for this band at 1.30 microns?

480 * 640 * 24 * 60 = 442 368 000 bits of bandwith is needed.

Problem №9:
Is the Nyquist theorem true for optical fiber or only for cooper wire?

It is true for all media.

Problem №18:
A simple telephone system consists of two end offices and a single toll office to which each end office is connected by a 1-MHz full-duplex trunk. The average telephone is used to make four calls per 8-hour workday. The mean call duration is 6 min. Ten percent of the calls are long-distance (i.e., pass through the toll office). What is the maximum number of telephones an end office can support? (Assume 4 kHz per circuit.)