Given the probability distributions shown to the right, complete the following p
ID: 2921897 • Letter: G
Question
Given the probability distributions shown to the right, complete the following parts.
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
Distribution A
Distribution B
X
P(X)
X
P(X)
0
0.030.03
0
0.530.53
1
0.110.11
1
0.190.19
2
0.140.14
2
0.140.14
3
0.190.19
3
0.110.11
4
0.530.53
4
0.030.03
Distribution A
Distribution B
X
P(X)
X
P(X)
0
0.030.03
0
0.530.53
1
0.110.11
1
0.190.19
2
0.140.14
2
0.140.14
3
0.190.19
3
0.110.11
4
0.530.53
4
0.030.03
Explanation / Answer
A) E(XA) = 0 * 0.03 + 1 * 0.11 + 2 * 0.14 + 3 * 0.19 + 4 * 0.53 = 3.08
E(XB) = 0 * 0.53 + 1 * 0.19 + 2 * 0.14 + 3 * 0.11 + 4 * 0.03 = 0.92
b) E(XA2) = 02 * 0.03 + 12 * 0.11 + 22 * 0.14 + 32 * 0.19 + 42 * 0.53 = 10.86
Var(XA) = E(XA2) - (E(XA))2 = 10.86 - 3.082 = 1.3736
SD(XA) = sqrt(1.3736) = 1.172
E(XB2) = 02 * 0.53 + 12 * 0.19 + 22 * 0.14 + 32 * 0.11 + 42 * 0.03 = 2.22
Var(XB) = E(XB2) - (E(XB))2 = 2.22 - 0.922 = 1.3736
SD(XB) = sqrt(1.3736) = 1.172
c) Stadard deviation is same for both the distribution. BUt mean is greater for distribution A
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