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Introduction to Statistical Thinking

Benjamin Yakir

Section 4.6 Exercises

Table 4.6.1. The Distribution of \(Y\)
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Value Probability
0 1p
1 2p
2 3p
3 4p
4 5p
5 6p

Checkpoint 4.6.2.

Table 4.6.1 presents the probabilities of the random variable \(Y\text{.}\) These probabilities are a function of the number \(p\text{,}\) the probability of the value “0”. Answer the following questions:
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  1. What is the value of \(p\text{?}\)
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  2. \(\Prob(Y < 3 )\) = ?
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  3. \(\Prob(Y = \mbox{odd})\) = ?
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  4. \(\Prob(1 \leq Y < 4)\) = ?
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  5. \(\Prob(|Y -3| < 1.5)\) = ?
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  6. \(\Expec(Y)\) = ?
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  7. \(\Var(Y)\) = ?
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  8. What is the standard deviation of \(Y\text{.}\)
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Checkpoint 4.6.3.

One invests $2 to participate in a game of chance. In this game a coin is tossed three times. If all tosses end up “Head” then the player wins $10. Otherwise, the player losses the investment.
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  1. What is the probability of winning the game?
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  2. What is the probability of loosing the game?
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  3. What is the expected gain for the player that plays this game? (Notice that the expectation can obtain a negative value.)
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