Question

QUESTION 6 Why is the following not a probability distribution? co to ox P(x) 0.11 0.19 0.43 0.17 0.25 The values of x are negative 4 The probability values are not increasing The probability values do not add to 1 The probability values are not discrete

Answer 1

QUESTION 6:
Correct option:

The probability values do not add to 1.

(1)

(a)

P(Wavy) = 43/215 = 0.2

(b)
P(Brown OR Straight) = P(Brown) + P(Straight) - P(Brown AND Straight)

                                   = 100/ 215 + 172/215 - 80/215

                                   = 192/215

                                 = 0.8930

(c)

P(Wavy AND Black) = 15/215 = 0.0698

(d)
P(Red/ Straight) = P(Red AND Straight)/ P(Straight)

                     = 12/172

                      = 0.0698

(3)

(a)

The probability distribution is finished as follows:

x	P(x)
1	0.35
2	0.20
3	0.15
4	0.15
5	0.1
6	0.05
Total =	1.00

(b)
From the above Table, the following Table is calculated:

x	p	x p	x2 p
1	0.35	0.35	0.35
2	0.20	0.40	0.80
3	0.15	0.45	1.35
4	0.15	0.60	2.40
5	0.1	0.5	2.5
6	0.05	0.3	1.8
Total =	1.00	2.6	9.2

(b)

(i) Expected Value = E(X) = 2.6

(ii) Variance = E(X²) - (E(X))² = 9.2 - 2.6² = 2.44

Standard deviation =

V2.44 = 1.5620

So,

Standard deviation = 1.5620

Variance = 2.44