Chapter 6

1. As the random variables are clearly independent, P(Tall, Rain) = P(Tall)P(Rain) = 0.75 • 0.2 = 0.15.
2. One of the main drawbacks of histograms is that when the number of bins is too large, many of them start to be empty, because there are no samples in all of the value ranges. In this case, either the cardinality of X can be smaller than 1,000, or, even with more than 1,000 samples, the relative frequencies can be concentrated in a number of bins smaller than 1,000.
3. The total number of samples is 75, and the bins have equal lengths. Hence, P(0 < x < 2) = 20/75 ≈ 0.27, P(2 < x < 4) = 30/75 = 0.4, and P(4 < x < 6) = 25/75 ≈ 0.33. As we don't have any samples, we can assume that P(x > 6) = 0; therefore, P(x > 2) = P(2 < x < 4) + P(4 < x < 6) ≈ 0.73. We have an immediate confirmation, considering that 0...