Q1. Let wI be the power received by the mobile at distance "I" from the base station. The probability distribution of the power at distance "I" is p(wI) = exp(-wI/mI )/mI where mI is the mean. Assume mI is proportional to I^-3. If 10log(mI /1 m watt) = -110dBm at I = 20km,

A) Find the probability of 10log10(wI/1m watt) > -115dBm.

B) Find the distance L, i.e., when I = L km, such that the probability of 10 log10 (wL/1m watt) >-100 dBm is exp(-1).

Q2. Let r1 and r2 be the signal strengths received by a mobile from base stations 1 and 2, respectively. The probability distribution of r1 and r2 are:

p(r1)=0.1, p(r2)=0.1, 0≤r1,r2≤10;

Assume r1 and r2 are independent random variables. When the mobiles are near the cell border, they can have adequate communication with more than one base station if r1/r2 <2 and r2/r1 <2. What is the probability that the mobile can have adequate communication with both base stations?

The received signal of a communication system r = s + N . Here, s is source information and takes the value of 1 or -1. N is the noise uniformly distributed in the interval of [-x +x].

a) If x is 0.5, what is the bit error rate (BER)?

b) If x is 1.5, what is the bit error rate (BER)?

Q3. Let y be a random variable with probability density function g(y)=0.5*sin(y) where π ≥ y ≥ 0. Let x be a random variable uniformly distributed in the interval: [0 1]. Express y in terms of x such that the CDF of y is equal to the CDF of x.