Probability, Statistical Independence, Population Structure and Confidence Interval

Running head: ASSIGNMENT 1 1

ASSIGNMENT 1 2
Question 1
a) Probability is the measure of the likelihood that an event will occur. Probability is
measured by defining the events of interests. Thereafter, the total number of events of
interest is divided by all possible outcomes. Probability measures ranges between 0 and
1. That is, given that probability is p(x), then 0 ≤ p (x)≤1. This means that the likelihood
of an event occurring ranges from 0% to 100%; no more, no less.
b) Statistical independence of the probability of a compound event composed of the
intersection of statistically independent events is the product of the probabilities of its
components.
c)
1.
Sales of Units
(x)
No. of
days p(x)
Exp
value
More
Than
Less
Than
[x-
E(x)]^2
[x-
E(x)]^2p(x)
0 5 0.05 0 0.95 0 0 0
1 15 0.15 0.15 0.8 0.05 0.7225 0.108375
2 20 0.2 0.4 0.6 0.2 2.56 0.512
3 25 0.25 0.75 0.35 0.4 5.0625 1.265625
4 20 0.2 0.8 0.15 0.65 10.24 2.048
5 15 0.15 0.75 0 0.85 18.0625 2.709375
Total 100 1 2.85
Varianc
e 6.643375
Std dev 2.57747453

ASSIGNMENT 1 3
9
Sales of
Units (x)
No. of
days p(x)
Exp
value More Than Less Than
[x-
E(x)]^
2
[x-
E(x)]^2
p(x)
0 5 =5/B8 =A2*C2
=C3+C4+C5
+C6+C7 0
=(A2-
D2)^2 =G2*C2
1 15 =15/B8 =A3*C3
=C4+C5+C6
+C7 =C2
=(A3-
D3)^2 =G3*C3
2 20 =B4/B8 =A4*C4 =C5+C6+C7 =C2+C3
=(A4-
D4)^2 =G4*C4
3 25 =B5/B8 =A5*C5 =C6+C7 =C2+C3+C4
=(A5-
D5)^2 =G5*C5
4 20 =B6/B8 =A6*C6 =C7
=C2+C3+C4
+C5
=(A6-
D6)^2 =G6*C6
5 15 =B7/B8 =A7*C7 0
=C2+C3+C4
+C5+C6
=(A7-
D7)^2 =G7*C7
Total 100
=SUM(
C2:C7)
=SUM(
D2:D7)
Varian
ce
=SUM(
H2:H7)
Std
dev
=SQRT(
H8)