Research Methods and Statistics 2019 Assignment 2022

1
Research Methods and Statistics 2019 Assignment 4
By (name)
Tutor
Course
Date
Question 1

2
P (A) – Probability oil is struck at location A = 0.5
P (B) – probability oil is struck at location B = 0.3
P (AB) – probability that oil is struck at both A and B = 0.2
i) Probability of A & B
Since A and B are not mutually exclusive,
P (A or B) = p(A) + p(B) – p(A and B) = (0.5 + 0.3) – 0.2 = 0.6
ii) Probability of A given B
P(A|B) = P ( A∧B)
P( B) = 0.2
0.3 =2
3
iii) Return
20 × P ( A ) +20 × P ( B )−10
¿ ( 20 ×0.5 )+ ( 20× 0.3 )−10
¿ 10 millionMatlab call function
For the conditional probability in (ii)
Question 2
i)
Assuming that a > b
4 ab= ( a+b ) 2− ( a−b )2
Assuming ( a+ b )2 ≫ ( a−b )2
4 ab< ( a+b ) 2
ab< ( a+b ) 2
4
√ab=(a+ b)
2
Let
m= loge a+ loge b
2 = 1
2 loge( ab)
m=loge( √ ab)

3
The geometric mean is,
GM = √ab=em=e
1
2 (loge a+loge b)
Matlab commands
X = [a, b]
Geometric mean = geomean(X)
Arithmetic mean = mean(X)
M = log ( a)+ log (b)
2Question 3
Probability of incoming mail sent to T=Probability of N sent to T or Probability
of U sent to T
P(T)=P(TU)+P(TN)
=(0.1*(1-0.35))+(0.35*(1-0.05)
=0.3975
ii.
p(TU)= Probability of U and T= (1-0.35)*(0.1)=0.065
Question 4
i)
Let the probability of good PCs be p
p= 3
5
The probability of PCs with hardware bugs be p '
p' = 2
5
P ( all good PCs )= 3
5 × 2
4 × 1
3 = 1
10
ii)
Let the probability of good PCs be p
p= 60
100
The probability of PCs with hardware bugs be p '
p' = 40
100