Answer:
[tex]V(X) = 2.45\ pts[/tex]
Step-by-step explanation:
We look for the expected value for a touchdown.
If X represents the number of points scored per touchdown scored, then X is a discrete random variable, and by definition, the expected value V (X) for a discrete random variable is defined as:
[tex]V(X) = \sum{XP(X)}[/tex]
Where P(X) is the probability that X will occur.
In the sample space of the random variable X there are two possible values.
[tex]X = 7[/tex] points (1 touchdown) with [tex]P(7) = 0.35[/tex]
[tex]X = 0[/tex] points (0 touchdown) with [tex]P(0) = 1-0.35 = 0.65[/tex]
Then the expected value V(X) is:
[tex]V(X) = 7P(7) + 0P(0)[/tex]
[tex]V(X) = 7(0.35) + 0(0.65)[/tex]
[tex]V(X) = 2.45\ pts[/tex]
