1) Expected Value: Expected value indiscrete random variable is a kind of mean o

Question

1)      Expected Value: Expected value indiscrete random variable is a kind of mean or average. It includesall expectations like loss and gain.

Formula: E(x) = ?[x * p(x)] = x

a)      Shawn and Maddie purchase aforeclosed property for $50,000 and spend an additional $27,000fixing up the property. They feel that they can resell the propertyfor $12,000 with probability 0.15, $100,000 with probability 0.45,$80,000 with probability 0.25, and $60,000 with probability 0.15.Compute and interpret the expected profit for reselling theproperty.

b)      Find the expected value of aplayer. When a player rolls a die if die face has 1, 2, 3 and 4 theplayer receives $20, $15, $10 and $5 respectively. However, playerhas to pay $15 for the rest of the faces. Interpret the expectedvalue. Is the game beneficial for the player? Why or why notexplain.

Please Explain, Thank You

Explanation / Answer

a) I assume you meant to say $120,000 instead of $12,000 for the .15 chance ofselling. The initial investment (the amount they paid for the house) is$50,000+$27,000=-$77,000 The expected value of the sale is(.15)($120,000)+(.45)($100,000)+(.25)($80,000)+(.15)($60,000)=$92,000 (with .15 chance of selling for $12,000 the expectedvalue is $75,800, in case that's what you meant) That means the expected profit is $92,000-$77,000=$15,000 or (-$1200 for the $12,000 thing, justin case you need it). b) The expected value is$20(1/6)+$15(1/6)+$10(1/6)+$5(1/6)+-$15(1/6)+-$15(1/6)=+$3.3333 It is beneficial to the player to play this game, because inthe long run, the average winings for each play will be about$3.33, so they will gain money.

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