SOLUTION: Please help me with this probability question.It is due tomorrow.
5. Consider the ‘symmetric’ distribution as shown in the table below, where a and b are any numbers between 0 and
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5. Consider the ‘symmetric’ distribution as shown in the table below, where a and b are any numbers between 0 and
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Question 349379: Please help me with this probability question.It is due tomorrow.
5. Consider the ‘symmetric’ distribution as shown in the table below, where a and b are any numbers between 0 and 1.
x=1 Pr(X)=b,x=2 Pr(X)=a,x=3 Pr(X)=a,x=4 Pr(X)=b
Prove that E(X)=2.5 Answer by Edwin McCravy(20056) (Show Source):
x P(x) x*P(x)
1 b b
2 a 2a
3 a 3a
4 b 4b
-----------------
Totals: 1 E(X)
The totals of the individual probabilities must be 1.
The totals of the individual expectations equals the
total expectation E(X).
Therefore
summing the middle column:
b + a + a + b = 1
2b + 2a = 1
2(b + a) = 1
b + a =
Summing the right-most column:
E(X) = b + 2a + 3a + 4b
E(X) = 5b + 5a
E(X) = 5(b + a)
Substituting for b + a,
E(X) = 5() = = 2.5
Edwin
