Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The expected number of days Pete will catch fish is
A).6
B).8
C)2.4
D)3

Question

Quizplus · Accepted Answer

The expected value of a discrete random variable is given by E(X) = ∑(x * P(X=x)).

In this case, X can take values 0, 1, 2, or 3. The probability that Pete catches fish on a given day is 0.8, and the probability that he doesn't catch fish is 0.2. Therefore,

E(X) = 0 * P(X=0) + 1 * P(X=1) + 2 * P(X=2) + 3 * P(X=3)
     = 0.2^3 * 0 + 0.2^2 * 0.8 * 1 + 0.2 * 0.8^2 * 2 + 0.8^3 * 3
     = 2.4

So the expected number of days Pete will catch fish is 2.4.

Exhibit 5-7 The Probability That Pete Will Catch Fish When He Goes