sta301 Assignment 2 solution Spring 2020

STA301 Assignment No.2 2021

 

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

Note.  X represents the number of heads

SOLUTION

SAMPLING:

HHHH

TTTT

HHHT

TTTH

HHTH

TTHT

HHTT

TTHH

HTHH

THTT

HTHT

THTH

HTTH

THHT

HTTT

THHH

Frequency Distribution:

No. of Heads 

       X

Value of the 4 Coins Flips

Total No. 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

      

        2

HHTT, HTHT, HTTH, THTH, THHT, TTHH

            6

  

   6/16

              12/16

        3

HHHT, HHTH, HTHH, THHH

            4

  4/16

              12/16

        4

HHHH

             1

  1/16

              4/16

MEANS

Mean=

Mean=

NOW FOR STANDARD ERROR WE FIND STANDARD DEVIATION 

X

X2

 P(X)

          X2. P(X)

0

0

 1/16

                0

1

1

 4/16

              4/16

2

4

 6/16

             24/16

3

9

 4/16

             36/16

4

16

 1/16

            16/16

STANDARD DEVIATION

Standard Deviation=

Standard Deviation= 

Standard Deviation=

Standard Deviation=

Standard Deviation=

STANDARD ERROR

Standard Error= 

Standard Error=1/

              Standard Error =1/2 =0.5