How many values can store a byte i.e. a sequence of 8 bits (1 bit=0,1).

Suppose to have a perfect random byte generator. What is the probability of have 11111111 as output? What is the probability of have 10110100?

If $x$ is random uniform number in $[-a,a]$ what is the probability of $y=e^{-kx}$?

With $x$ and $y$ defined in the previous point all the moments of $x$ exists, therefore all the moments of $y$ exists. Is this statement true?

What is the difference between isothermal and adiabatic transformation.

A damped harmonic oscillator of mass $m$ and oscillator characteristic frequency $\omega$ initially departs with initial velocity $v_0=0$ from the poit which is displace by $\ell$ from the equilibrium position. After some time we found it at rest. What is the work done by the damping force on the system?

Consider a transformation in a perfect classical gas. By halving the pressure we get a doubling of the volume? Which transformation we have performed?

$N$ independent two level systems are thermalized at a given temperature T. What is the ratio between the average number of systems in the higher energy level and that on the lower?

What is the Maxwell-Boltzmann distribution?

What are the Bose-Einstein and Fermi-Dirac distributions.