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Expected value of a random variable
- a)is always positive
- b)may be positive or negative
- c)may be positive or negative or zero
- d)can never be zero
Correct answer is option 'C'. Can you explain this answer?
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Expected value of a random variablea)is always positiveb)may be positi...
The expected value of a random variable is the weighted average of the values that can take on, where each possible value is weighted by its respective probability. The expected value of a random variable is denoted by and it is often called the expectation of or the mean of .
The two expected values will have the same magnitude but differ in sign. Using your terminology, a negative expected value would indeed be better for the casino (the player would 'expect' to lose a little money, so the casino would gain money).
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Expected value of a random variablea)is always positiveb)may be positi...
Explanation:
The expected value of a random variable is a measure of the central tendency of the variable. It is defined as the weighted average of all possible values that the variable can take, with the weights given by the probabilities of each value occurring.
The expected value can be positive, negative or zero depending on the distribution of the random variable.
Examples:
- If the random variable is a fair coin toss, which can take the values of either heads or tails with equal probability, the expected value is (1/2)x1 + (1/2)x0 = 1/2. This is a positive value.
- If the random variable is the outcome of rolling a fair six-sided die, which can take the values 1, 2, 3, 4, 5 or 6 with equal probability, the expected value is (1/6)x1 + (1/6)x2 + (1/6)x3 + (1/6)x4 + (1/6)x5 + (1/6)x6 = 3.5. This is a positive value.
- If the random variable is the amount of money gained or lost in a fair game of roulette, which has a negative expected value due to the presence of the green 0 and 00 pockets.
Therefore, the correct answer is option c) may be positive or negative or zero.
The expected value of a random variable is a measure of the central tendency of the variable. It is defined as the weighted average of all possible values that the variable can take, with the weights given by the probabilities of each value occurring.
The expected value can be positive, negative or zero depending on the distribution of the random variable.
Examples:
- If the random variable is a fair coin toss, which can take the values of either heads or tails with equal probability, the expected value is (1/2)x1 + (1/2)x0 = 1/2. This is a positive value.
- If the random variable is the outcome of rolling a fair six-sided die, which can take the values 1, 2, 3, 4, 5 or 6 with equal probability, the expected value is (1/6)x1 + (1/6)x2 + (1/6)x3 + (1/6)x4 + (1/6)x5 + (1/6)x6 = 3.5. This is a positive value.
- If the random variable is the amount of money gained or lost in a fair game of roulette, which has a negative expected value due to the presence of the green 0 and 00 pockets.
Therefore, the correct answer is option c) may be positive or negative or zero.
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Expected value of a random variablea)is always positiveb)may be positive or negativec)may be positive or negative or zerod)can never be zeroCorrect answer is option 'C'. Can you explain this answer?
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