STA301 - Statistics and Probability Assignment No 2 Solution Spring 2021

 

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Requirement:

Toss a fair coin four times and construct frequency distribution for the (Raise For Success) number of heads.  Also find the mean and standard error of that probability distribution of heads.

Note.  X represents the number of heads.




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Solution:

HHHH, HHHT, HHTH, HHTT, (Raise For Success) HTHH, HTHT, HTTH, HTTT, TTTT, TTTH, TTTH, TTHT, TTHH, THTT, THTH, THHT, THHH


Frequency distribution:


Number of Heads X

Value of the 4 coin Flips

Total Number of ways of getting a Heads

P(X)

X.P(X)

0

TTTT

1

1/16

0

1

HTTT, THTT, TTHT,TTTH

4

4/16

4/16

(Raise For Success)

2

HHTT, HTHT, HTTH, THTH, THHT, TTHH

6

(Raise For Success)

6/16

12/16

3

HHHT, HHTH, HTHH, (Raise For Success) THHH,

4

4/16

12/16

4

HHHH

1

1/16

4/16

 

 

 

 

32/16 = 2



Mean = 32/16 =2
Now for standard error we find standard deviation:

X

X^2

P(X)

X^2.P(X)

0

0

1/16

0

1

1

4/16

(Raise For Success)

4/16

2

4

6/16

24/16

3

(Raise For Success)

9

4/16

36/16

(Raise For Success)

4

16

1/16

16/16

 

 

 

 

80/16 = 5


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