The mean of uniform distribution with parameter a and b is
(a) b-a (b)b+a (c) (a+b)/2 (d) (b-a)/2
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Answer:
The notation for the uniform distribution is X ~ U(a, b) where a = the lowest value of x and b = the highest value of x.
The probability density function is
f
(
x
)
=
1
b
−
a
f(x)=1b−a for a ≤ x ≤ b.
For this example, X ~ U(0, 23) and
f
(
x
)
=
1
23
−
0
f(x)=123−0 for 0 ≤ X ≤ 23.
Formulas for the theoretical mean and standard deviation are
μ
=
a
+
b
2
and
σ
=
√
(
b
−
a
)
2
12
μ=a+b2andσ=(b−a)212
For this problem, the theoretical mean and standard deviation are
μ
=
0
+
23
2
=
11.50
seconds
and
σ
=
√
(
23
−
0
)
2
12
=
6.64
seconds
μ=0+232=11.50 secondsandσ=(23−0)212=6.64 seconds
Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.
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