Answer:
For the variance we need to calculate first the second moment given by:
And after solve the integral we got:
And for this case the variance would be:
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 w ehave the following density function:
We can determine the mean with the following integral:
And if we solve the integral we got:
For the variance we need to calculate first the second moment given by:
And after solve the integral we got:
And for this case the variance would be:
And the deviation would be: