Question:Find the probability that X(1), X(2).....X(n) is a permutation of 1,2....n when X(1), X(2).....X(n) are independent and each is equally likely to be any of the values 1,2....n. Solution I assume the meaning of \"permutation of 1,2,...n\" means that the digits 1 through n can be selected in any order, but all must be present precisely once. For the first digit you can select any one of the n numbers. For the second digit you can select any one of the remaining (n- 1) numbers that have not yet been picked - the probability of doing so is (n-1)/n. For the third number there are (n-2) numbers remaining that haven\'t been picked yet, so the probability of picking a \"good\" number is (n-2)/n. And so on..

1. Question:
Give one example for each of the three generations of cellular systems, and list the multiple
access techniques used by the sample systems.
Solution
The examples of three generations of cellular systems are:
1)
Second generation systems (2G): This generation includes technologies like GSM(Global
System of Moblie communications),GPRS(Global Packet Radio Service) and EDGE(Enhanced
Data for GSM Evolution).
The latter two are only software updations of GSM.
GSM being the main player of this technology uses TDMA (Time division multiple access)
technique. Though internally in the BTS(Base Transciever systems) it also uses FDMA to alot
single frequency to 8 users. But overall system is based on time synchorinaztion hence it is a
TDMA system.
2)
Third generation systems (3G): This technology was introduced to increase the data carrying
capablity of the telecom systems by increasing the potential bandwidth. This was done by using
W-CDMA (Wide band code divison multiple access). Since there is no interference with CDMA
even at same frequencies, the net bandwidth hence speed of data communication increased.
3)
Fourth generation (4G): This technology is IP based. It uses OFDMA (Orthogonal frequency
divison multiple access) technique. When distributing bandwidth, some guard bands are left on
account of filters used in technology, as filter never has an ideal response. OFDMA uses
orthogonal frequencies which do not interfere with each other, even if the overlap. Hence in 4G
guard bands are also used to transmit data, increasing net transfer rate.