00:01
To calculate the pdf of x and the probability that x is between 1 and 3, we first need to find the pdf of x and then integrate it over the given range.
00:09
X represents the received signal when we do not have any weather information.
00:14
So we have amplitude of transmitted signal, s equals 2, weather conditions, good, variance of noise where the standard deviation squared equals 1, and bad, variance of noise, standard deviation squared equals 4.
00:42
And those are equally likely.
00:45
So let's calculate a pdf of x.
00:52
So x is the received signal and is equal to the sum of the transmitted signal s and the noise w.
00:59
The mathematical form would be x equals little s plus w.
01:05
To calculate the pdf of x, we need to consider the convolution of the pds of s and w.
01:11
S is a constant, 2, its pdf is a direct delta function at 2.
01:17
The pdf of w in good weather is normal with 0 mean and variance 1, and in bad weather it has a 0 mean and variance 4...