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Korolek [52]
3 years ago
9

A dealer decides to sell an antique card by means of an English auction with a reservation price of $200. There are two bidders.

The dealer believes that there are only two possible values, $200 and $600, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/2 of having each of these willingness to pay, and the probabilities for each of the three bidders are independent of the others' valuations. Assuming that the three bidders bid rationally and do not collude, the dealer's expected revenue from selling the card is approximately ____.
Mathematics
1 answer:
Vinvika [58]3 years ago
6 0

Answer:

Expected revenue = $400

Step-by-step explanation:

Expected revenue is given by the formula;

Expected revenue = Sum of x * p(x)

x = 200

x = 600

p(x) = 1/2

p(x) = 1/2

Substituting, we have;

Expected revenue = 200*1/2 + 600*1/2

                               = 100 + 300

                                = $400

Therefore, expected revenue = $400

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<h3>What does summation mean in math?</h3>

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

<h3>Briefing:</h3>

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

<h3>Calculation according to the statement:</h3>

\sum_{j=1}^{200} 2 j(j+3)

simplifying them we get:

\sum_{j=1}^{200} 2 j^{2}+6 j

Split the summation into smaller summations that fit the summation rules.

\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j

\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}

The formula for the summation of a polynomial with degree 2

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\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}

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(2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$

we get: 5373400

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Add the results of the summations.

5373400 + 120600

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The sum of the equation is  = 5494000.

To know more about  summations visit:

brainly.com/question/16679150

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1 year ago
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