Question 697399: Find the mean and standard deviation of the following probability distribution:
x/P(x) 1/0.3 2/0.3 3/0.4
please somebody walk me through this
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! The mean of this distribution is equal to the sum of the products of each result and their respective probabilities. For this distribution, the mean is
1*(.3) + 2*(.3) + 3*(.4) = 2.1.
The standard deviation of a distribution is equal to the square root of its variance. To find the variance of a discrete probability distribution such as this, you can use the formula:
Variance = E[X^2] - (E[X])^2
E[X] refers to the expected value of x, and is a fancy way to refer to the mean of the distribution. E[X^2] thus refers to the mean of the squares of the distribution. It is calculated similarly, except the values are 1, 4, and 9 instead of 1, 2, and 3:
E[X^2] = (1^2)*(.3) + (2^2)*(.3) + (3^2)*(.4) = 1*(.3) + 4*(.3) + 9*(.4) = 5.1.
E[X] was found earlier; it is 2.1. So, (E[X])^2 = 2.1^2 = 4.41.
Variance = E[X^2] - (E[X])^2 = 5.1 - 4.41 = .69.
The standard deviation is the square root of the variance, or  = .8307.
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