Suppose you're in the game show. There're 4 prizes hidden on 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. (Describe 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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What is your expected winning in this game? (Show work and round the answer to two decimal places)
What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)