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Given the following probability distributions:
Distribution C X P{X = Xi)
0 1 2 3 4
0 0.20 0.20 0.20 0.20
Distribution D X P{X = Xi)
0 1 2 3 4
0 0.10 0.40 0.20 0.10
A. Compute the expected value for each distribution.
B. Compute the standard deviation for each distribution.
C. Compare the results of distributions C and D.

Respuesta :

Answer:

Step-by-step explanation:

The expected value of this distribution will be the Mean

upon calculation

For the distribution of C

1)   P(x=xi)  0    1          2        3       4

              0    0.20   0.20  0.20  0.20

[tex]Mean = Pi*xi[/tex]

           = 0*0+1*0.2+2*0.2+3*0.2+4*0.2

Mean    = 2

2) Standard deviation of C

        [tex]\sqrt{(xi-mean)^2 *P(xi)}[/tex]

        = 1.09

For the distribution of D

1)       P(x=xi)    0    1       2      3      4

                     0    0.1   0.4   0.2  0.1

[tex]Mean = Pi*xi[/tex]

          = 1.9

2) Standard deviation

       = 0.984

Upon comparing the result we observe that

C has greater expected value than D

C has greater standard deviation than D which means it is more spreading of the given data than D.

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