Innehåll 1 Sannolikhetsteori - Matematikcentrum

1 SANNOLIKHETSTEORI
p Y
(y)
f X
(x)
0.7
a
0.3
0 25 35
y (m)
0 5 10 15 20
x, Increase in Water Level in Reservoir B
(a) Determine the value of a in the bottom right figure.
(b) What is the probability of overflow at B during a strong-motion earthquake
(c) If there were no overflow at B during an earthquake, what is the probability that the original
water level in reservoir B is 25 m
21. [∗] The bearing capacity of the soil under a column-footing foundation is known to vary between 6
and 15 kN/m 2 . Its probability density (täthetsfunktion) within this range is given as
{ 1
f X (x) = 2.7 (1− x ), 6 ≤ x ≤ 15
15
0, elsewhere
If the column is designed to carry a load of 7.5 kN/m 2 , what is the probability of failure of the
foundation
22. Den tid som en kraft belastar en viss konstruktion varierar
på ett sätt som beskrivs av täthetsfunktionen i
figuren.
(a) Bestäm konstanterna a och b.
f T
(t)
b
a t 2
(b) Beräkna väntevärde och median för belastningstiden
T .
(c) Beräkna sannolikheten att T är minst 6 sek, dvs
P(T ≥ 6).
0 12 16
t, sec.
23. The delay time of a construction project is described with a random variable X . Suppose that X is
a discrete variate with probability mass function (sannolikhetsfunktionfunktion) given in the table.
The penalty for late completion of the project depends on the number of day of delay; that is,
penalty = g(x i ). The penalty function is also given in the table, in unit of $100, 000.
PMF of X Penalty funktion
x i p X (x i ) g(x i )
(in days) ($100, 000)
1 0.5 5
2 0.3 6
3 0.1 7
4 0.1 7
6