Assume that the population of a city (in some unit) is a random variable X with density (1/ 22x)e(log(x)10)^2 /8 1(x>0) . We recall that log is the natural logarithm (in base e).

1. Identify the density function fY (y) of the random variable Y = log X.

2. Using the table in Appendix, compute P(X > 500000).

3. Let us pick independently ten cities. What is the probability that at most three cities have a population greater than 500,000 people?