Implement the following function to create a matrix of dimensionality numRows x numCols, where matrix starts with an initial size of 0. Furthermore, initialize the value at matrix [i][j] to the product of i and j.

void matrixInit( vector< vector >& matrix, int numRows, int numCols);

For example, if numRows is 3, numCols is 4, you are going to allocate space to matrix so that it contains three row vectors, where the size of each row vector will be 4. At the end of this function call, the content of matrix will be:

size of matrix is: 3x4

matrix[0][0]=0
matrix[0][1]=0
matrix[0][2]=0
matrix[0][3]=0
matrix[1][0]=0
matrix[1][1]=1
matrix[1][2]=2
matrix[1][3]=3
matrix[2][0]=0
matrix[2][1]=2
matrix[2][2]=4
matrix[2][3]=6

Hint: This task requires memory management. Please refer to a C++ reference manual to identify the relevant member functions. Keep in mind that a function such as push_back() also involves memory management.

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?