The number of movies shown in different theatres on Saturday morning in a small city is given in the following.
x P(x)
1 0.15
2 0.20
3 0.30
4 0.10
What is the mean distribution (or expectation) of the data given above?
To find the mean distribution or expectation of the data provided, we need to calculate the weighted average of the number of movies and their probabilities.
The formula for calculating the mean is:
Mean = Σ (x * P(x))
Where x represents the number of movies, and P(x) represents the probability of that number of movies.
Let's calculate the mean distribution step by step:
1. Multiply each value of x with its corresponding probability, P(x):
1 * 0.15 = 0.15
2 * 0.20 = 0.40
3 * 0.30 = 0.90
4 * 0.10 = 0.40
2. Sum up the results:
0.15 + 0.40 + 0.90 + 0.40 = 1.85
Therefore, the mean distribution or expectation of the data provided is 1.85.
This means that, on average, there are 1.85 movies shown in different theaters on a Saturday morning in the small city.