Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semester. Value of X 3 4 5 6Probability 0.07 0.4 0.25 0.28What are the mean and the standard deviation of the number of courses full-time students at this college take this semester?

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: