Fall 2010 (Total Marks 30)
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23:59 29th November, 2010
Assignment No.2 (Lessons 12 to 18)
Question 1
2
5=10Marks
2
5=10Marksa)
On which basis
Chebychev's
inequality and empirical rules are dissimilar?
b)
Why we calculate measure of skewness and kurtosis?
c)
For what purpose simple linear equation is used? Also explain the drawback of the simple linear equation.
d)
Differentiate between an experiment and a random experiment.
e)
In deterministic experiment, can we apply probability theory? Explain.
Question 2
3+2+5=10Marks
3+2+5=10Marks
a)
Suggest the skewness of the data from the following information.
b)
For a certain data:
Mean = 62.83, Median = 61.5
And Standard Deviation = 8.516
Find mode and Pearson's coefficient of skewness
c)
Find the first four moments about mean from the following data.
X= 14, 20, 22, 34, 30, 18, 26, 28, 16, 25
Question 1
8+2+=10Marks
8+2+=10Marks
a)
For following data calculate
i.
simple linear equation Y on X
simple linear equation Y on X
ii.
simple linear equation X on Y
simple linear equation X on Y
iii.
From the slops calculated in above cases, calculate coefficient of correlation.
From the slops calculated in above cases, calculate coefficient of correlation.
Hight=X
5.6
5.2
5.5
6.0
6.1
5.0
5.4
5.2
5.3
5.6
5.1
Weight=Y
67
65
66
75
69
62
64
68
65
65
62
b)
How many different words can be formed from the word 'BLOGOSPHERE'?
..........
Solution:
Question1: A:
On which basis Chebychev's inequality and empirical rules are dissimilar?
Empirical Rule and Chebychev Inequality
If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87. There is no contradiction between empirical rule and Chebychev Inequality
Q NO 1: C
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
Linear regression implements a statistical model that, when relationships between the independent variables and the dependent variable are almost linear, shows optimal results.
Linear regression is often inappropriately used to model non-linear relationships.
Linear regression is limited to predicting numeric output.
A lack of explanation about what has been learned can be a problem.
Linear Regression Software Solutions
QNO1: D
In an experimental study, the reasearcher manipulates on of the variables and tries to determine how the manipulation influences other variables.
A Random Experiment is an experiment, trial, or observation that can be repeated numerous times under the same conditions. The outcome of an individual random experiment must be independent and identically distributed. It must in no way be affected by any previous outcome and cannot be predicted with certainty.
Examples of a Random experiment include:
•The tossing of a coin. The experiment can yield two possible outcomes, heads or tails.
•The roll of a die. The experiment can yield six possible outcomes, this outcome is the number 1 to 6 as the die faces are labelled
•The selection of a numbered ball (1-50) in an urn. The experiment can yield 50 possible outcomes.
•Percentage of calls dropped due to errors over a particular time period. The experiment can yield several different outcomes in the region 0 - 100%.
On which basis Chebychev's inequality and empirical rules are dissimilar?
Empirical Rule and Chebychev Inequality
If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87. There is no contradiction between empirical rule and Chebychev Inequality
Q NO 1: C
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
Linear regression implements a statistical model that, when relationships between the independent variables and the dependent variable are almost linear, shows optimal results.
Linear regression is often inappropriately used to model non-linear relationships.
Linear regression is limited to predicting numeric output.
A lack of explanation about what has been learned can be a problem.
Linear Regression Software Solutions
QNO1: D
In an experimental study, the reasearcher manipulates on of the variables and tries to determine how the manipulation influences other variables.
A Random Experiment is an experiment, trial, or observation that can be repeated numerous times under the same conditions. The outcome of an individual random experiment must be independent and identically distributed. It must in no way be affected by any previous outcome and cannot be predicted with certainty.
Examples of a Random experiment include:
•The tossing of a coin. The experiment can yield two possible outcomes, heads or tails.
•The roll of a die. The experiment can yield six possible outcomes, this outcome is the number 1 to 6 as the die faces are labelled
•The selection of a numbered ball (1-50) in an urn. The experiment can yield 50 possible outcomes.
•Percentage of calls dropped due to errors over a particular time period. The experiment can yield several different outcomes in the region 0 - 100%.
