Find the Standard Deviation table[[x,P(x)],[five , three],[six , twelve],[seven , fifteen],[eight , eleven],[nine , three]]

Find the Standard Deviation table[[x,P(x)],[5,3],[6,12],[7,15],[8,11],[9,3]]
Prove that the given table satisfies the two properties needed for a probability distribution.
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A discrete random variable takes a set of separate values (such as , , ...). Its probability distribution assigns a probability to each possible value . For each , the probability falls between and inclusive and the sum of the probabilities for all the possible values equals to .
1. For each , .
2. .
is not less than or equal to , which doesn't meet the first property of the probability distribution.
is not less than or equal to
is not less than or equal to , which doesn't meet the first property of the probability distribution.
is not less than or equal to
is not less than or equal to , which doesn't meet the first property of the probability distribution.
is not less than or equal to
is not less than or equal to , which doesn't meet the first property of the probability distribution.
is not less than or equal to
is not less than or equal to , which doesn't meet the first property of the probability distribution.
is not less than or equal to
The probability does not fall between and inclusive for all values, which does not meet the first property of the probability distribution.
The table does not satisfy the two properties of a probability distribution
The table does not satisfy the two properties of a probability distribution
The table does not satisfy the two properties of a probability distribution, which means that the standard deviation can't be found using the given table.
Can't find the standard deviation
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