Consider the r.v. X from Exercise 41 replacing 0 by a small number . Compare 1/E{X} and

Consider the r.v. X from Exercise 41 replacing 0 by a “small” number ε. Compare 1/E{X}
and E{1/X}. Which theorem does this example illustrate?

Exercise 41

Does the fact that E{X} has a “moderate” value, mean that X cannot assume “big” values?
Let us consider a r.v.

for large n. Such a r.v. may illustrate a possible future loss connected with a possibility of a catastrophic event, say, an earthquake. The probability of the event is small, but the damage, if the event occurs, is large. Compute E{X} and comment on to what extent in this case the mean value reflects the “behavior” of the r.v.