ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 162  165 of 165
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Question number: 162
» Probability » Distribution Function » Standard Probability Distributions
Appeared in Year: 2011
Describe in Detail
Show that is a probability density function for an appropriate value of a. Upto what order do the moments of this p. d. f. exist?
Explanation
To find the value of a, we known that the probability density function under the range of x is equal to one.
To find order which is exist for this p. d. f. is
Upto moments is exist is k2 < 0 =
Question number: 163
» Numerical Analysis » Interpolation Formulae » Gauss
Appeared in Year: 2009
Describe in Detail
Find the value of
by taking 5 subintervals and using the Trapezoidal rule.
Explanation
Let
First divided the interval into 5 subintervals
x  0  1/4  1/2  3/4  1 
y  1  16/17  4/5  16/25  ½ 
Here a = 0, b = 1, n = 4, h= (ba) /n = 1/4
the Trapezoidal rule is
Question number: 164
» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)
Appeared in Year: 2015
Describe in Detail
By making use of difference table and a suitable interpolation formula, find the number of student who obtained less than 45 marks in an examination, from the following table
Marks  30  40  40  50  50  60  60  70  70  80 
Number of students  31  42  51  35  31 
Explanation
Applying NewtonGregory forward formula for interpolating the number of student who obtained less than 45 marks in an examination.
Marks less than  Number of student  Difference  
∆y _{0}  ∆ ^{2} y _{0}  ∆ ^{3} y _{0}  ∆ ^{4} y _{0}  
x _{0} =40  y _{0} = 31  42  9 
25 
Question number: 165
» Statistical Methods » Association and Contingency
Appeared in Year: 2015
Describe in Detail
Compute Yule’s coefficient of association (Q) and Yule’s coefficient of colligation (Y) for the following table:
 Disease onset  

 Yes  No 
Medicine used  A  19  587 
B  193  2741 
Explanation
The frequencies for various attributes be show in this contingency table
Medicine used  Yes (A)  No (a) 
A (B)  (AB)  (aB) 
B (b)  (Ab)  (ab) 
(i) Yule’s coefficient of association is a relative measure of association between two attributes, for this question the attributes are NoTB and treatment. If (AB),