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How do you calculate the expectation value and standard deviation when you have multiple probabilities?
Wiki User
∙ 10y ago
Suppose the discrete variable X takes the values x where the x belong to some set A. So, for example, if X is the result of a roll of a die then A = {1, 2, 3, 4, 5, 6}.
Then the expected value of X,
E(X) = Sum of [x*Prob(X = x)], where the summation is over all x in A.
In the die example, this would be
1*Prob(X=1) + 2*Prob(X=2) + ... + 6*Prob(X=6)
Let E(X2) = Sum of [x2*Prob(X = x)], where again the summation is over all x in A.
Then Variance(X) = E(X2) - [E(X)]2
and the Standard Deviation = sqrt(Variance).
If X is a continuous variable, then replace Prob(X = x) by the probability density function of X and instead of the summation over A, you will need to integrate with respect to x over the set A.
Wiki User
∙ 10y ago
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What is the probability of the multiple of three?
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What is a 1.66 standard deviation in percentage?
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Calculate lowest common multiple of 18 24 and 27?
The lowest common multiple of the numbers 18, 24 and 27 is 216.
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2
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