k c2(k) = -(-1)* = -1½[1+ (–1)*] + c2, i=0
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
explain this step please
![Example C
The second-order, inhomogeneous equation
(k + 4)yk+2 + Yk+1 – (k + 1)Yk = 1
(3.97)
has the following two solutions:
1
(1)
(3.98)
(k + 1)(k + 2)*
(2)
(-1)k+1|
k+1(2k + 3)
(3.99)
4(k + 1)(k + 2)
to its associated homogeneous equation
(k + 4)yk+2 + Yk+1
(k + 1)yk = 0.
(3.100)
These functions have the Casoratian
(-1)k+1
(k + 2)(k + 3)(k + 4)
C(k +1)
(3.101)
The particular solution takes the form
(1)
Yk = c1 (k)y + c2(k)y,.
(3.102)
Direct calculation shows that c1(k) and c2(k) satisfy the equations
Acı (k) = 1/4(2k + 5),
Ac2(k) = (-1)*+1,.
(3.103)
Summing these expressions gives
k
c1(k) = 14 (2i + 5) +¢1 = /4(k + 1)² + c1
(3.104)
i=0
and
k
c2(k)
E(-1)' = -1/½[1 + (-1)*]+c2,
(3.105)
i=0
where ci
and
c2 are arbitrary constants. Substituting equations (3.98), (3.99),
(3.104), and (3.105) into equation (3.102) and dropping the terms that contain
the arbitrary constants gives
k +1
4(k + 2)
(2k + 3)[1+(-1)*]
8(k + 1)(k + 2)
(3.106)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2c2145d-bd1f-45a0-9330-175afc112391%2Feb6a757e-6af3-45c9-8335-4dba5e8b7766%2Frnop8qw_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps
