STA301 Assignment%232

8/6/2019 STA301 Assignment%232

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Assignment No.2 (Course STA301)

Spring 2011 (Total Marks 30)

Question 1: Marks: 2+2+4+2=10a. By using five number summary, suggest the skewness of the data from the

following information:

Xm 55,X0 25,Q2 39

Solution: Q2 X0 39 25 14

XmQ2 55 39 16

Distance between Q2 -X0 is less than Xm -Q2,

so it is positively skewed

b. For a certain data,

m1 0, m2 2.64, m3

5.6

and m4 28.30

Find moment ratios b1 and b2 . Interpret your results also.

Solution:MOMENTS RATIOS

m

2

b

and...b m

41

m 3 2 m

22 2

5.62

b and...b

28.302

1

2.64 2.64 31.36 28.30

b and b

1 18.399...

2

6.969

b1=1.70 and b2=4.06 answer

INTERPRETATION OF b1Our distribution is positively skewed, m3 will be positive and our distribution is


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negatively skewed, m3 will be negative. b m3

INTERPRETAION OF b2

For a normal distribution, b2=3

1

m 3

c.Explain equally likely events with the help of an example.

Answer: two events A and B are said to be equally likely, when one event is as likely

to occur as the other.

Example: When a fair coin is tossed, the head is as likely to appear as the tail, and theproportion of times each side is expected to

appear is 1/2.

Question 2: Marks: 4+4+2=10

a. For a particular

data of 5 pair ofvalues:

Y2

2 6 ,

Y 1 0 ,

X Y 3 7

The fitted regression line is:

Y= -1.5 + 0.5 x

Find the standard error of estimate (Sy.x); what doest it indicates?

Solution:

syx

Y2 aYbXY

n 226 1.5 10 0.537

5 2

7.5

=2.73 answer

b. Five yellow balls and four green balls, which are indistinguishable apart from

color, are placed in a bag if six balls are taken from the bag; Find the probability

of being three yellow and three green.


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Solution :

n !

n1!.n2!.n3!.........

6!

3!X3!6X5X4X3X2X1

6X6

72036

=20 answer

c. If the equations of the least square regression lines are:

Y= -1 + 0.5 x And X= -1.1 + 0.2 y

Find correlation coefficient r.Solution : r

0.31Answer

byxb

xy

0.50.2 0.1

Question 3: Marks: 5+5=10

a.

i. How many different words (even meaningless) can be formed from the word

Component?

Solution:C comes ones so n1= 1

O comes twice n2=2

M comes ones so n3=1

P comes ones so n4=1N comes twice n5=2

E comes ones so n6=1

T comes ones so n7=1

n!

n1 !.n2 !.n3 !.n4 !.n5 !.n6 !.n7 !

9!

1!2!1!1!2!1!1!

=90720answer


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ii. How many distinct four-digit numbers can be performed from the following

integers 2, 3,4,5,6 where each integer is used only once?

Solution:

n1=5

n2=4

n3=3

n4=2

5X4X3X2=120 answer

b. When a pair of dice is rolled, make the sample space and find the probabilityi) Total of 5

Solution :

SAMPLE SPACE{(1.1), (1.2), (1.3), (1.4), (1.5), (1.6)

(2.1), (2.2), (2.3), (2.4), (2.5), (2.6)

(3.1), (3.2, (3.3, (3.4), (3.5), (3.6)

(4.1), (4.2), (4.3), (4.4), (4.5), (4.6)

(5.1), (5.2), (5.3), (5.4), (5.5), (5.6)

(6.1), (6.2),(6.3), (6.4), (6.5), (6.6)}

PROBABILITY OF TOTAL 5 ISn(A)=(1.4 , 2.3, 3.2,4.1,)n(S)=36

n(A)

n(S)4

36

=0.11 answer

ii) Total of 7?

PROBABILITY OF TOTAL 7=?

Let B be the event that sum of outcome is equal to 7

n(A)={1.6, 2.5, 3.4, 4.3, 5.2, 6.1}

n(A)=6

n(S)=36


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n(A)

n(S)

6

36

0.16answer

STA301 Assignment%232

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