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Problem:
Random models can be very effective tools to study real world networks. This question considers creating a simple random network N. We start with 100 nodes v1; v2;... v100 with no links between them. Then for each pair (i; j) of integers satisfying 1 <=i < j <= 100 we roll a fair 6-sided die. If the die roll is a 1, 2, 3 or 4 we take no action. On a roll of 5 or a 6 we add a link between vi and vj . When we add a link it goes in both directions, so vj is also linked to vi. Let X be the random variable that counts the total number of unordered choices for two nodes that have a link between them. Let Y be the random variable that counts the number of nodes linked to v1 in N.
Required:
(a) How many times do we roll the die in order to create N?
(b) Find E[X].
(c) What type of probability distribution does Y have?
Calculate the integer part of the quotient when integer a is divided by integer b. Calculate the integer remainder when integer a is divided by integer b.
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