The random variable X, representing the number of items sold in a week, has the following probability distribution: Values of a Random Variable X x 0 1 2 3 4 5 6 P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 On average, how many items are sold in a week? Don't forget to show your work.
Question
The random variable X, representing the number of items sold in a week, has the following probability distribution: Values of a Random Variable X x 0 1 2 3 4 5 6 P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 On average, how many items are sold in a week? Don't forget to show your work.
Solution
To find the average number of items sold in a week, we need to calculate the expected value (E[X]) of the random variable X. The expected value is calculated by multiplying each possible value of X by its corresponding probability and then summing these products.
Here's how to do it:
E[X] = Σ [x * P(X = x)]
= (0 * 0.10) + (1 * 0.20) + (2 * 0.40) + (3 * 0.15) + (4 * 0.05) + (5 * 0.05) + (6 * 0.05)
= 0 + 0.20 + 0.80 + 0.45 + 0.20 + 0.25 + 0.30
= 2.20
So, on average, 2.20 items are sold in a week.
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