obability that half of the atoms have decayed after one minute? Probability distributions 2.3 (B): What is the probability of counting five heads after tossing a coin ten times? 2.4 (B): Assume that 10% of the population contracted the flu. Taking 20 people at random, what is the probability of finding three people with the flu? What is the probability of finding not more than three? 2.5 (M): Show that the mean and standard deviation of a uniform, continuous PDF defined over the real interval [Xmin, Xmax] of finite width Ax are <x> = (Xmax + xmin)/2 and o = Ax/ 12, respectively. 2.6 (B): Calculate the mean and variance of the exponential distribution p(x) = de-2x (x > 0, 2 > 0). 2.7 (B): A brand of TV set has a mean time to failure (MTFF) of five years with a warranty of one year. What is the probability that the TV set will fail before the warranty expires? What is the probability of a failure happening between one and five years? 2.8 (B): Assume that, every year, there are 50 car accidents per 1000 new drivers, following an exponential law. What is the probability that a new driver will: (a) Have one car accident after 2 years? (b) Have no accident over 5 years? (c) Have at least one accident between 2 and 5 years? 2.9 (T): Prove that the mean and variance of the Bose-Einstein distribution are <n> = N and o2=N+N2,1 respectively. 2.10 (T): Prove that the mean and variance of the Poisson distribution satisfy <n> = N=02. Measuring information In effect, the concept of information is obvious to anyone in life. Yet the word captures SO much that we may doubt that any real definition satisfactory to a large majority of either educated or lay people may ever exist. Etymology may then help to give the word some skeleton. Information comes from the Latin informatio and the related verb informare meaning: to conceive, to explain, to sketch, to make something understood or known, to get someone knowledgeable about something. Thus, informatio is the action and art of shaping or packaging this piece of knowledge into some s