Answer to Question #304222 in Statistics and Probability for PleaseAnswerThis

Question

Calculate the mean, variance, and standard deviation. Show your solution.

1. X P(X)

1 0.11

2 0.49

3 0.33

4 0.07

2. X P(X)

2 2/10

4 3/10

6 4/10

8 1/10

3. X P(X)

1 0.25

3 0.13

4 0.35

6 0.27

Answer 1

1.We find the mean as below

mean = ( (1*0.11) + (2*0.49) +(3*0.33) + (4*0.07) ) = 2.36

we define the variance as below

variance =( (1²* 0.11) + (2² * 0.49) + (3² *0.33) + (4²*0.07) ) - (mean)²

= (6.16 - 5.5696 ) = 0.5904

standard deviation = (variance)^1/2 = (0.5904)^1/2 = 0.768374908

2.We define the mean as below

mean = ( (2 * 2/10) + (4 * 3/10) + (6 * 4/10) + (8 * 1/10) ) = 4.8

we define the variance as below

variance = ( (2²* 2/10) + (4² * 3/10) + (6² * 4/10) + (8² * 1/10) ) - (mean)²

= (26.4 - 23.04) = 3.36

standard deviation = (variance)^1/2 = (3.36)^1/2 = 1.833030278

3.We define the mean as below

mean = ( (1* 0.25) + (3* 0.13) + (4 * 0.35) + (6 * 0.27) ) = 3.66

we define the variance as below

variance = ( (1² * 0.25) + ( 3² * 0.13) + (4² * 0.35) + (6² * 0.27) ) - (mean)²

=(16.74 - 13.3956) = 3.3444

standard deviation = (variance)^1/2 = (3.3444)^1/2 = 1.828770078