of departure u(0) ¼u
0
and its initial velocity v(0) ¼v
0
off the bow are random variables
with probability density functions
f
u
0
(u) N(m
u
0
, s
u
0
), 1 < u < 1 (5:147)
f
v
0
(u) U[(v
0
)
L
, (v
0
)
U
], (v
0
)
L
v (v
0
)
U
(5:148)
where
m
u
0
and s
u
0
are the mean and standard deviation of the Normal population
(v
0
)
L
and (v
0
)
U
are the lower and upper limits of the Uniform population
A Monte Carlo experiment can be designed to estimate the probability of hitting the target.
‘‘Chap5_MonteCarlo_arrow.m’’ uses the MATLAB functions ‘‘rand’’ and ‘‘randn’’ to generate
random deviates R
i
U(0, 1) and z
i
N(0, 1). R
i
and z
i
are transformed to random deviates from the
desired populations, Equations 5.147 and 5.148 by
(u
0
)
i
¼ m
u0
þ z
i
s
u
0
(5:149)
(v
0
)
i
¼ (v
0
)
L
þ [(v
0
)
U
(v
0
)
L
]R
i
(5:150)
For now, ...