The random variable X, representing the number of items sold in a week, has the following probability distribution:x 0 1 2 3 4 5 6P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05On average, how many items are sold in a week? 6.3 3.0 2.2 2.0 0.1428
Question
The random variable X, representing the number of items sold in a week, has the following probability distribution:x 0 1 2 3 4 5 6P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05On average, how many items are sold in a week? 6.3 3.0 2.2 2.0 0.1428
Solution 1
To find the average number of items sold in a week, we need to calculate the expected value of the random variable X. The expected value (E[X]) is calculated by multiplying each outcome by its probability and then summing these products.
Here's how to do it:
E[X] = (0 * 0.10) + (1 * 0.20) + (2 * 0.40) + (3 * 0.15) + (4 * 0.05) + (5 * 0.05) + (6 * 0.05)
E[X] = 0 + 0.20 + 0.80 + 0.45 + 0.20 + 0.25 + 0.30
E[X] = 2.2
So, on average, 2.2 items are sold in a week.
Solution 2
To find the average number of items sold in a week, we need to calculate the expected value of the random variable X. The expected value (E[X]) is calculated by multiplying each outcome by its probability and then summing these products.
Here's how to do it:
E[X] = (0 * 0.10) + (1 * 0.20) + (2 * 0.40) + (3 * 0.15) + (4 * 0.05) + (5 * 0.05) + (6 * 0.05)
E[X] = 0 + 0.20 + 0.80 + 0.45 + 0.20 + 0.25 + 0.30
E[X] = 2.2
So, on average, 2.2 items are sold in a week.
Solution 3
To find the average number of items sold in a week, we need to calculate the expected value of the random variable X. The expected value (E[X]) is calculated by multiplying each outcome by its probability and then summing these products.
Here's how to do it:
E[X] = (0 * 0.10) + (1 * 0.20) + (2 * 0.40) + (3 * 0.15) + (4 * 0.05) + (5 * 0.05) + (6 * 0.05)
E[X] = 0 + 0.20 + 0.80 + 0.45 + 0.20 + 0.25 + 0.30
E[X] = 2.2
So, on average, 2.2 items are sold in a week.
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