Given the following sampling distribution: X -17 -9 -5 5 19 P(X) 7 100 7 100 1 2

Question

Given the following sampling distribution:

X

-17

-9

-5

5

19

P(X)

7100

7100

120

3100

___

What is the mean of this sampling distribution?

a) 13.2

b) 1.4

c) 12.8

d) 0.3

e) 12.9

f) None of the above

Suppose you have a distribution, X, with mean = 6 and standard deviation = 2. Define a new random variable Y = 8X - 3. Find the mean and standard deviation of Y.

a) E[Y] = 45; Y = 16

b) E[Y] = 45; Y = 128

c) E[Y] = 45; Y = 13

d) E[Y] = 48; Y = 13

e) E[Y] = 48; Y = 128

f) None of the above

X

-17

-9

-5

5

19

P(X)

7100

7100

120

3100

___

Explanation / Answer

as total of probabilty =1

also P(X=-5)=1/20=5/100

hence P(X=19) =1-(7+7+5+3)/100=78/100

therefore mean =(-17)*(7/100)+(-9)*(7/100)+(-5)*(5/100)+5*(3/100)+19*(78/100)=12.9

option e is correct

2) E(Y)=8*E(X)-3 =8*6-3=45

std deviation of Y=8*std deviation of X =8*2=16

therefore option A

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