EN330 – Probability and Statistics with Ocean Applications
Analysis of Random Processes
Practice of Basic Skills
1. Given the water surface elevation data below, find:
a. H
b. H s
c. H rms
d. What is the relationship between the statistics for η and H?
20
15
10
η (ft)
5
0
-5
-10
-15
-20
0
5
10
15
20
25
t (s)
30
35
40
2. What probability distribution does the water surface elevation (η) follow?
3. What probability distribution does wave height (H) follow?
4. If H rms = 12 ft , what is the probability of H > 24 ft?
45
50
5. If σ = 4 ft, what is the probability of -4 ft < η < 4 ft?
6. Data are acquired over a period of 120 s at a sampling rate of 20 Hz.
a. What is the lowest frequency component that can be resolved?
b. What is the highest frequency component that can be resolved?
7. Given the wave energy spectrum below taken during storm conditions in the Gulf of
Mexico, find:
a. m0
b. Hs
c. σ
d. What frequency and period has the largest contribution to the wave energy?
e. An offshore platform is placed in this area of the G of M. What deck
elevation is required so that the deck is above the water surface 99.9% of the
time in these conditions?
2000
1800
1600
S(f) (ft2/Hz)
1400
1200
1000
800
600
400
200
0
0
0.05
0.1
0.15
f (Hz)
0.2
0.25
0.3