of movies 0 1 2 3 4

To find the expected number of movies Val watches per month, we use the concept of expected value. The formula for expected value $E(X)$ when dealing with a discrete probability distribution is:

$E(X) = \sum (x_i \cdot P(x_i))$

Where:

• $x_i$ is each possible value (in this case, the number of movies).
• $P(x_i)$ is the probability of each corresponding $x_i$.

Here, the possible values for $x_i$ are $0, 1, 2, 3, 4$ and the probabilities $P(x_i)$ are $0.12, 0.10, 0.20, 0.42, 0.16$, respectively.

Now, let's compute the expected value:

$E(X) = (0 \cdot 0.12) + (1 \cdot 0.10) + (2 \cdot 0.20) + (3 \cdot 0.42) + (4 \cdot 0.16)$

$E(X) = 0 + 0.10 + 0.40 + 1.26 + 0.64 = 2.40$

Thus, the expected number of movies Val watches per month is 2.40.

Would you like further details or have any questions? Here are some related questions:

1. What does an expected value of 2.40 mean in practical terms?
2. How would the expected value change if one of the probabilities was different?
3. What is the variance of the number of movies Val watches per month?
4. How can we use this model to predict the total number of movies over a year?
5. How does expected value apply to decision-making in real life?

Tip: The expected value is an average, meaning Val is likely to watch around 2-3 movies a month, even though she cannot watch a non-integer number of movies!