Statistics Assignment-2 (Weeks: 5-7) | Desklib

CSTS-SEU-KSA
___________________________________________________________________
Statistics (STAT-101)
Assignment-2 (Weeks: 5-7)
1st Semester, 1439-1440 (2018-2019)
Due date: 20/10/2018 (Time: 10:30 PM)
Student’s Name
Student’s ID
Section/CRN
Location
Marking Scheme
Question Score Obtained Score
Q-1 3
Q-2 3
Q-3 3
Q-4 3
Q-5 3
Q-6 3
Total 18
Note: You are required to fill your full name, ID and CRN.
Solution to the Questions

CSTS-SEU-KSA
Question One
a. Probability distribution table for the random variable
Solution
Type of a Coin Frequency
f
Probability
p= f
∑ f
$ 1 2 0.22
$ 5 3 0.33
$ 10 1 0.11
$ 20 3 0.33
Total(∑) 9 1.00
b. Variance.
According to Hassett & Stewart (2006), the variance is given by the formula
Var ( x ) =E ( x2 )−¿ ¿
¿ ∑ x2 ¿ px− ( ∑ x∗px )
2
The table below summarizes the result of the computation
Type of a Coin Frequency
f
x=coin $∗f Probability
px
x∗px x2∗px
$ 1 2 2 0.22 0.444 0.889
$ 5 3 15 0.33 5.000 75
$ 10 1 10 0.11 1.111 11.111
$ 20 3 60 0.33 20.000 1200
Total(∑) 9 1.00 26.556 1287

CSTS-SEU-KSA
Therefore,
¿ ∑ x2 ¿ px− (∑ x∗px )2
=1287− ( 26.556 )2
¿ 1287−705.198=581.802 .
Therefore, the variance is $ 581.80
Question Two
Solution
The probability of interest is P rob ( x ≥3 ) =1−P ( x <3 )
The distribution of the 5 students adopts binomial distribution with probability of
success( p ) of an event been 0.13 and that of failed ( q ) event is 0.87. The number of
independent trials ( n ) is 5 and the number of success 3or more ( r )
According to Hassett & Stewart (2006), the probability of success in a binomial
distribution is given by
P rob ( x=r ) = [ n
r ] ( p ) r ( q ) n −r
Therefore,
P rob ( x ≥3 ) =1−P rob ( x< 3 )
¿ 1− { P rob ( x=0 ) + P rob ( x=1 ) + P ( x=2 ) }