Question

X	1	2	3	4	5
P(X)		0.2	0.3	0.1	0.3

a) Finish the probability table

b) Define Y = -2X+6 .

c) Calculate E(X) Std(X) E(Y) Std(Y)

Answer 1

PART A.

X P(X)

1 -

2 0.2

3 0.3

4 0.1

5 0.3

We knew that probability of an event will be as equal to 1

following this rule, Sum of P(X) = 1 and assume the missing value is 'X'

=> X + 0.2 + 0.3 + 0.1 + 0.3 = 1

=> X + 0.9 = 1

=> X = 1 - 0.9

=> X = 0.10

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PART B.

Y = -2X+6

for X =1 , Y = -2(1)+6 = 4

=> X =2 , Y = -2(2)+6 = 2

=> X =3 , Y = -2(3)+6 = 0

=> X =4 , Y = -2(4)+6 = -2

=> X =5 , Y = -2(5)+6 = 4

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PART C.

For X Mean, SD

∑ f= 1

∑ fx = 3.3

Mean = ∑ fx / ∑ f = 3.3

Mean square =∑ f x^2 / ∑ f = 12.7

Variance = (Mean square) - (Mean)^2

Variance = ? f x^2 - Mean^2 = 1.81

Stadard Dev= v Var = 1.345

For Y Mean, SD

Mean = Sum of observations/ Count of observations

Mean = (4 + 2 + 0 + -2 + 4 / 5) = 1.6

Variance

Step 1: Add them up

4 + 2 + 0 + -2 + 4 = 8

Step 2: Square your answer

8*8 =64

…and divide by the number of items. We have 5 items , 64/5 = 12.8

Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time

4^2 + 2^2 + 0^2 + -2^2 + 4^2 = 40

Step 4: Subtract the amount in Step 2 from the amount in Step 3

40 - 12.8 = 27.2

Step 5: Subtract 1 from the number of items in your data set, 5 - 1 = 4

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance

27.2 / 4 = 6.8

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation

2.6077