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, we can calculate the product of each value of x (the number of movies) with its corresponding probability P(x) and sum them up.
Let's calculate:
Mean distribution = (x₁ * P(x₁)) + (x₂ * P(x₂)) + (x₃ * P(x₃)) + (x₄ * P(x₄))
= (1 * 0.15) + (2 * 0.20) + (3 * 0.30) + (4 * 0.10)
= 0.15 + 0.40 + 0.90 + 0.40
= 1.85
Therefore, the mean distribution or expectation of the given data is 1.85.