Problem 10 Let U be a random variable that has a uniform distribution on [0, 1]. We set X = ln(Y). Show that X follows an exponential distribution and find its parameter. Problem 11 The lifespan of the Radon atom follows an exponential distribution. The probability that un atom does not desintegrate in 40 seconds knowing that it did not desintegrate in 12 seconds is Q. What is the probability that the atom will not disintegrate before 76 seconds knowing that it will not do it in 20 second? Problem 11 A Telecom service provider claims that individual customers pay on an average 400$ per month with standard deviation of 25$. A random sample of 50 customers bills during a given month is taken with a mean of 250 and standard deviation of 15. What to say with respect to the claim made by the service provider? Problem 12 From the data available, it is observed that 400 out of 850 customers purchased the groceries online. Can we say that most of the customers are moving towards online shopping even for groceries