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Consider a box model with one 1 and nine 0s.If there are 16 draws with replacement from the box, what is the expected value for the sum?Group of answer choices1.6160.160.1

Question

Consider a box model with one 1 and nine 0s.If there are 16 draws with replacement from the box, what is the expected value for the sum?Group of answer choices1.6160.160.1

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Solution

The expected value (E) of a random variable is the sum of the probability of each outcome times the value of that outcome. In this case, the box model has one 1 and nine 0s, so the probability of drawing a 1 is 1/10 and the probability of drawing a 0 is 9/10.

The expected value for a single draw from the box is therefore:

E = (1/10)*1 + (9/10)*0 = 0.1

Since there are 16 draws with replacement (meaning the probabilities don't change from draw to draw), the expected value for the sum of the draws is simply 16 times the expected value for a single draw:

E_sum = 16E = 160.1 = 1.6

So, the expected value for the sum of 16 draws with replacement from the box is 1.6.

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