Problem 3: Write a recursive function getGCD to calculate the greatest common denominator of two given numbers. For example, getGCD( 12, 9) = 3. The function should have the following declaration: function gcd = getGCD( n1, n2) where inputs n1 and n2 are positive integers and output gcd is the greatest common denominator of n1 and n2. The function should have a description. When the inputs are not positive integers, set the output to be a string 'Error' and use return to exit the function. (a) Set p3a = evalc('help getGCD').

Consider a slotted aloha system, where the time slot equals the fixed duration of each packet. assume that there are 4 stations a,b,c,d sharing the medium. (a) stations a,b,c,d receive one packet each from higher layers at times 1.3, 1.5, 2.6,5.7 respectively. show which transmissions take place when, according to the slottedaloha protocol; describe all transmissions until all four packets have been successful.when needed, each station has access to the following sequence of random number, provided by a random number generator and drawn uniformly between 0 and 1: (1) station a draws numbers: 0.31, 0.27, 0.78, 0.9, 0.9, 0.11, 0. (2) station b draws numbers: 0.45, 0.28, 0.11, 0.83, 0.37, 0.22, 0. (3)station c draws numbers: 0.1, 0.2, 0.3, 0.4, 0. (4) station d draws numbers: 0.36, 0.77, 0.9, 0.1, 0.1, 0.1, 0.1, 0. (b) in slotted aloha, a station transmits in each time slot with a given probability. what probabilities would you assign to each of the four stations so as to: (i) maximize the efficiency of the protocol? (ii) maximize fairness among the four stations? (c) will the efficiency increase or decrease if we modify slotted aloha as follows: (i) get rid of slots and allow stations to transmit immediately? (ii) implement carrier sensing? (iii) implement collision detection? (iv) implement collision avoidance?

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Assume the existence of a bankaccount class. define a derived class, savingsaccount that contains two instance variables: the first a double, named interestrate, and the second an integer named interesttype. the value of the interesttype variable can be 1 for simple interest and 2 for compound interest. there is also a constructor that accepts two parameters: a double that is used to initialize the interestrate variable, and a string that you may assume will contain either "simple", or "compound", and which should be used to initialize the interesttype variable appropriately. there should also be a pair of functions getinterestrate and getinteresttype that return the values of the corresponding data members (as double and int respectively).