To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation(1) with μ = 5 and (A) μ = 10 (B) μ = 15 (C) μ = 20 Graph all three in the same viewing window with X min = − 10 , X max = 40 , Y min = 0 and Y max = 0.1
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation(1) with μ = 5 and (A) μ = 10 (B) μ = 15 (C) μ = 20 Graph all three in the same viewing window with X min = − 10 , X max = 40 , Y min = 0 and Y max = 0.1
Solution Summary: The author analyzes the equation of normal distribution. f(x)=1sigma
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean
µ
and standard deviation
σ
:
f
x
=
1
σ
2
π
e
−
x
−
μ
2
/
2
σ
2
Graph equation(1) with
μ
=
5
and
(A)
μ
=
10
(B)
μ
=
15
(C)
μ
=
20
Graph all three in the same viewing window with
X
min
=
−
10
,
X
max
=
40
,
Y
min
=
0
and
Y
max
=
0.1
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
Suppose a population of devices has a Weibull life distribution with β= 1.6 and θ= 25. What is the mean of the residual life distribution for copies of the device that survive 15 hours?
The following data are annual 15-min peak rainfall intensities I (in./hr) for 9 years of record. Compute and plot the log,,-normal frequency curve and the data. Use the Weibull plotting position formula. Using both the curve and the mathematical equation estimate (a) the 25-yr, 15-min peak rainfall intensity; (b) the return period for an intensity of 7 in./hr; (c) the probability that the annual maximum 15-min rainfall intensity will be between 4 and 6 in./hr.
Problem 2. Show that
D₁ = (DFFITS;)²
MSE (1)
(p+1)MSE'
where MSE() is the mean squared error after the i-th data point is omitted.
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