The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:x 0 1 2 3 4 5P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05On average, how many accidents are there in the intersection in a week? 5.3 2.5 1.8 0.30 0.1667
Question
The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:x 0 1 2 3 4 5P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05On average, how many accidents are there in the intersection in a week? 5.3 2.5 1.8 0.30 0.1667
Solution
To find the average number of accidents in the intersection in a week, we need to calculate the expected value of the random variable X. The expected value (E[X]) of a discrete random variable is calculated by summing the product of each outcome and its probability.
Here's how to calculate it:
E[X] = (0 * 0.20) + (1 * 0.30) + (2 * 0.20) + (3 * 0.15) + (4 * 0.10) + (5 * 0.05)
E[X] = 0 + 0.30 + 0.40 + 0.45 + 0.40 + 0.25
E[X] = 1.8
So, on average, there are 1.8 accidents in the intersection in a week.
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