Suppose you're in game show. There're 4 prizes hidden upon a game board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are worth $1000. You've to pay $50 to the host if your choice isn't correct. Let the random variable x be the winning.
Complete the following probability distribution. (Show the probability in fraction format and explain your work)
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x
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P(x)
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-$50
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$1,000
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$1,500
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$4,000
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Determine your expected winning in this game? (Show work and round the answer to two decimal places)
Determine the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)