STA301 Assignment # 4 Solution

STA301 Paper

STA301 Paper 26-05-2010

Total Questions: 26

Sample point with example

Calculate Standard Deviation and Variance

What is Coefficient of determination?

The Sample Space for tossing dice two times find probability (Handouts Page 147 Example 3 )

STA301

STA301 Assignment Solution:

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STA301

STA301 Assignment # 7 Solution:

Word Formate Solution:

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STA301

STA301 Assignment # 6 Solution:
Word Formate:
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STA301 Assignment Solution:

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STA301 Assignment Solution:
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STA301 Assignment_5 Solution:
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STA301 GDB

STA301 GDB Answer

It depends on the situation which we are considering.Just consider the example of Exams. Let suppose 25 candidates are appearingin an intelligence test and the average score of those 25 candidates comesout to be 55. Now in such situation the candidates who have scored betterthan the average score are definitely superior than the one who got belowaverage score.Another example is that I will give you of cricket matches. Let we supposethe average bowling average at any particular ground is 25. Now is someonehas taken wickets at that particular venue at say 20 runs per wicket. Thenwe can not say that the bowler who has picked up wickets at an average of 20at that venue is superior because it depends on so many situations. May bethe wickets he picked were against weaker sides. May be the weather at whichhe played was cloudy (which is helpful for bowlers). So in such situationswe cannot say someone superior.The summary of the above discussion is that we can say someone superior ifthe situation we are considering is EQUAL for every one. i.e. in case ofexam, every one had the same paper.When situation is NOT EQUAL for every one, then we cannot say someonesuperior, just as the example of cricket I gave above, which is certainlynot equal for every one.

STA301

STA301 3rd Assignment Solution

Q No. 1 (a): In how many ways can 4 boys and 5 girls sit in a
row if every boy and girl has to sit side by side?
In order to fulfill the given condition, the seating arrangement must be as
follows.
GIRL BOY GIRL BOY GIRL BOY GIRL BOY GIRL
5 girls can seat in 5 × 4 × 3 × 2 × 1 = 120 ways
4 boys can seat in 4 × 3 × 2 × 1 = 24 ways
Total number of ways in which 5 girls and 4 boys can sit fulfilling the
given condition = 120 × 24 = 2880
Q No. 1 (b): Briefly explain the terms mutually exclusive
events, exhaustive events and sample space.
Mutually Exclusive Events: Those events that cannot occur at the same
time.
Example: When we toss the coin, we get either Heads or Tails but not both.
Exhaustive Events: Events are said to be collectively exhaustive, when the union of mutually exclusive events is the entire sample space.
Example: When we toss a coin, then Heads and Tails are collectively known as Exhaustive Events.
Sample Space: Sample Space is a set which consists of all possible outcomes resulting from a random experiment
Example: Sample Space in case of a fair die is S = {1,2,3,4,5,6}
Q No. 1 (c): A fair coin is tossed. Make a sample space and find
the probability of the followings:
I. One head appears
II. One tail appears
III. No head appears
The sample space for a toss is S = {Heads, Tails}
One head appears = . = 0.5
One tail appears = . = 0.5
No head appears = . = 0.5
Q No. 2 (a): In a simple linear regression yˆ = a + bx , interpret the
coefficients “a” and “b”.
a is called the y-intercept, and b indicates the rate of change in y with
respect to x and is formally known as the slope of the line.
Q No. 2 (b): A computer while computing the correlation
coefficient between two variables x and y from 25 pairs of
observations, obtained the following results:
n = 25 , Σx = 125 , Σx2 = 650 , Σy = 100 , Σy2 = 460 , Σxy = 508
It was, however discovered at the time of re-checking that it
had mistakenly copied down two pairs of observations as
below:
x y
11 10
9 7
While the correct values were
x y
14 8
12 9
Now find out the correct value of correlation coefficient
between x and y.
Correct Σx = 125 – 11 – 9 + 14 + 12 = 131
Correct Σy = 100 – 10 – 7 + 8 + 9 = 100
Correct Σx2 = 650 – 112 – 92 + 142 + 122 = 788
Correct Σy2 = 460 – 102 – 72 + 82 + 92 = 456
Correct Σxy = 508 – (11 × 10) – (9 × 7) + (14 × 8) + (12 × 9) = 555

= 0.41

STA301

STA301 Solution:

Q No. 1 (a): In how many ways can 4 boys and 5 girls sit in a
row if every boy and girl has to sit side by side?
In order to fulfill the given condition, the seating arrangement must be as
follows.
GIRL BOY GIRL BOY GIRL BOY GIRL BOY GIRL
5 girls can seat in 5 × 4 × 3 × 2 × 1 = 120 ways
4 boys can seat in 4 × 3 × 2 × 1 = 24 ways
Total number of ways in which 5 girls and 4 boys can sit fulfilling the
given condition = 120 × 24 = 2880
Q No. 1 (b): Briefly explain the terms mutually exclusive
events, exhaustive events and sample space.
Mutually Exclusive Events: Those events that cannot occur at the same
time.
Example: When we toss the coin, we get either Heads or Tails but not both.
Exhaustive Events: Events are said to be collectively exhaustive, when the union of mutually exclusive events is the entire sample space.
Example: When we toss a coin, then Heads and Tails are collectively known as Exhaustive Events.
Sample Space: Sample Space is a set which consists of all possible outcomes resulting from a random experiment
Example: Sample Space in case of a fair die is S = {1,2,3,4,5,6}
Q No. 1 (c): A fair coin is tossed. Make a sample space and find
the probability of the followings:
I. One head appears
II. One tail appears
III. No head appears
The sample space for a toss is S = {Heads, Tails}
One head appears = . = 0.5
One tail appears = . = 0.5
No head appears = . = 0.5
Q No. 2 (a): In a simple linear regression yˆ = a + bx , interpret the
coefficients “a” and “b”.
a is called the y-intercept, and b indicates the rate of change in y with
respect to x and is formally known as the slope of the line.
Q No. 2 (b): A computer while computing the correlation
coefficient between two variables x and y from 25 pairs of
observations, obtained the following results:
n = 25 , Σx = 125 , Σx2 = 650 , Σy = 100 , Σy2 = 460 , Σxy = 508
It was, however discovered at the time of re-checking that it
had mistakenly copied down two pairs of observations as
below:
x y
11 10
9 7
While the correct values were
x y
14 8
12 9
Now find out the correct value of correlation coefficient
between x and y.
Correct Σx = 125 – 11 – 9 + 14 + 12 = 131
Correct Σy = 100 – 10 – 7 + 8 + 9 = 100
Correct Σx2 = 650 – 112 – 92 + 142 + 122 = 788
Correct Σy2 = 460 – 102 – 72 + 82 + 92 = 456
Correct Σxy = 508 – (11 × 10) – (9 × 7) + (14 × 8) + (12 × 9) = 555

= 0.41