The energy in arbitrary units of any individual particle in

The energy (in arbitrary units) of any individual particle in systems A, B and C is an independent continuous random variable X whose density is uniform from 1 to 2. The total energy in any of the systems is simply the sum of the energy of the individual particles. Find the probabilities using the most accurate technique. Evaluate your numerical expressions as far as possible without using a calculator.

System A contains 1,200 particles. Find the probability that the total energy in system A is between 1,790 and 1,808.

Solution

A is uniform from 1 to 2

A contains 1200 particles.

Hence each particle can give energy from 1 to 2

For 1790<X<1808

Prob = (1808-1790)/1200 = 0.015