Answer:
In order to find the variance we need to calculate first the second moment given by:
And the variance is given by:
And the deviation would be:
Step-by-step explanation:
Previous concepts
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 have the following distribution given:
X 3 4 5 6
P(X) 0.07 0.4 0.25 0.28
We can calculate the mean with the following formula:
In order to find the variance we need to calculate first the second moment given by:
And the variance is given by:
And the deviation would be: