RANDOM SIGNAL ANALYSIS 1 X and Y are both uniform over 01 Th

RANDOM SIGNAL ANALYSIS:

1. X and Y are both uniform over [0,1]. Therefore, X + Y is uniform over [0,2]

TRUE OR FALSE?

Solution

Answer is True.

Explaination: matlab code

for i=1:100
x(i)=rand;
y(i)=rand;
z(i)=x(i)+y(i);
end
>> z

z =

Columns 1 through 9

1.2601 0.7443 0.9113 0.6729 1.2027 0.9752 0.4439 1.0038 1.4290

Columns 10 through 18

1.9406 0.7887 0.6555 0.9015 0.1128 1.1485 1.5789 0.8303 0.4717

Columns 19 through 27

1.4420 0.7804 1.0627 0.3299 0.5164 1.1137 1.5017 1.5645 1.5345

Columns 28 through 36

0.0113 0.8613 0.8619 0.9636 1.6346 0.6255 0.8712 1.4791 0.3482

Columns 37 through 45

1.3792 1.0377 1.5365 0.7309 1.0188 0.8919 0.3365 0.9284 1.3277

Columns 46 through 54

0.4279 0.1415 0.8507 0.5750 0.9438 1.6527 1.0052 1.2686 0.4604

Columns 55 through 63

1.1035 0.6612 1.3721 0.3383 1.5940 0.4226 0.6120 1.3608 0.7497

Columns 64 through 72

0.5140 1.8721 0.4332 0.3507 0.9899 0.9328 1.7026 1.6208 0.9001

Columns 73 through 81

1.1758 1.0813 1.4268 0.2234 0.9511 0.8232 1.3478 1.6567 1.3624

Columns 82 through 90

1.4220 1.0836 0.6109 1.5681 0.5892 1.2100 0.9074 0.4137 1.1481

Columns 91 through 99

0.2810 1.7579 0.9747 0.5703 1.1509 0.5987 1.0032 0.1182 1.2136

Column 100

0.5743

based on result z is uniform over [0,2]