SOLUTION: <pre>Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
please walk me through this
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Algebra ->
Probability-and-statistics
-> SOLUTION: <pre>Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
please walk me through this
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Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
please walk me through this
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(A)
x P(x)
1 1/5
2 9/25
3 2/5
4 1/25
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(B)
x P(x)
3 0.7
6 1/12
8 0.22
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(C)
x P(x)
20 13/25
30 0.25
40 -0.01
50 6/25
We have to check just two requirements:
(1) All the probabilities in the P(x)
list must be between 0 and 1 inclusive.
(2) The sum of the probabilities in
the P(x) list must equal to 1.
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(A)
x P(x)
1 1/5
2 9/25
3 2/5
4 1/25
It meets the requirements of (1). Let's
check requirement (2)
Get LCD of 25
=
= 1, so yes it is a
probability distribution.
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(B)
x P(x)
3 0.7
6 1/12
8 0.22
It meets the requirements of (1). Let's
check requirement (2)
Change the decimals to fractions
Get LCD of 300
≠ 1, so NO it is NOT a
probability distribution.
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(C)
x P(x)
20 13/25
30 0.25
40 -0.01
50 6/25
It does NOT meet requirement (1), because of
the negative number in the probability list,
so it is NOT a probability distribution
function.
Edwin