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Answer:
Now we can calculate the second moment with the following formula:
And replacing we got:
And the variance is given by:
And replacing we got:
And the standard deviation is just the square root of the variance:
Step-by-step explanation:
Previous concepts
For this case we define the random variable X =" how many children the couple will have" and we know the following distribution:
X 1 2 3
P(X) 0.52 0.250 0.230
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
Solution to the problem
For this case we can find the expected value with the following formula:
And replacing we got:
Now we can calculate the second moment with the following formula:
And replacing we got:
And the variance is given by:
And replacing we got:
And the standard deviation is just the square root of the variance: