X= 5 X= 10 X= 15 Y= 10 0.05 0.10 Y= 20 0.10 0.25 0.20 Y= 30 0.05 0.15 0.10 The joint probability mass function due to an earthquake at a given location is shown in the table above. X is for landslide in (mm) Y is for aftershock (cubic meter per second; cms)- discretized for simplicity 1. What is the probability that the next earthquake will bring a landslide of 10 mm or less and of less than 20 cms? 2. After an earthquake, the gauge indicates a landslide of 15 mm. What is the probability that the aftershock in this earthquake is 20 cms or more? 3. Are landslide and aftershock statistically independent? Substantiate your answer, write your complete justification. 4. Determine the correlation between landslide and aftershock. Interpret the result. 5. If landslide is 10 mm, what is the expected aftershock (cms) and what is the standard deviation?

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