A sensor net work consists of n sensors that are distributed randomly on the unit square. Each node's location is uniform over the unit square and is independent of the locations of the other node. A node is isolated if there are no nodes that are within distance r of that node, where 0

1. Show that the probability that a given node is isolated is less than or equal to 

2. Using the union bound, find an upper bound on the probability that the sensor network contains at least one isolated node. 

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= (1-²)(n-1). 4 I) Pd