Compute the mean (μx) variance (σ2x) and standard deviation (??) of each sampling distribution. 1. When 100 independent samples are takenX1234thf(x)1/123/124/123/122. When 4 independent samples are takenX0123f(x)1/51/51/51/53. When 25 samples are drawn with replacementY2PP(y)1/21/64. When 64 samples are drawn with replacementZ3579F (Z)0.60.10.20.15. When 36 samples are drawn with replacementr102020| 27F (1)3/74/76. A random sample of size 30 taken from a population of 1000 with μ-20 and ²=9.7. A random sample of size 80 taken from a population of 10000 with μ=46.5 and a²=16.8. A random sample of size 45 taken from a population of 900, with μ=18.25 and ²=81.9. A random sample of size 64 taken from a population of 1200 whose μ =72.12 and σ= 12.10. A random sample of size 36 taken from a population of 3200 whose μ = 28.6 and σ= 54.4.31/351/1241/5

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Compute the mean (μx) variance (σ2x) and standard deviation (??) of each sampling distribution.

1. When 100 independent samples are taken
X
1
2
3
4
th
f(x)
1/12
3/12
4/12
3/12
2. When 4 independent samples are taken
X
0
1
2
3
f(x)
1/5
1/5
1/5
1/5
3. When 25 samples are drawn with replacement
Y
2
P
P(y)
1/2
1/6
4. When 64 samples are drawn with replacement
Z
3
5
7
9
F (Z)
0.6
0.1
0.2
0.1
5. When 36 samples are drawn with replacement
r
10
20
20
| 27
F (1)
3/7
4/7
6. A random sample of size 30 taken from a population of 1000 with μ-20 and ²=9.
7. A random sample of size 80 taken from a population of 10000 with μ=46.5 and a²=16.
8. A random sample of size 45 taken from a population of 900, with μ=18.25 and ²=81.
9. A random sample of size 64 taken from a population of 1200 whose μ =72.12 and σ= 12.
10. A random sample of size 36 taken from a population of 3200 whose μ = 28.6 and σ= 54.4.
3
1/3
5
1/12
4
1/5

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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