A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean of X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true?

k: 1 2 3 4 5
P(X=k): 0.1 0.2 0.4 0.2 0.1

Question

A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean of X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true?

k: 1 2 3 4 5
P(X=k): 0.1 0.2 0.4 0.2 0.1

Accepted Answer

Both the student and the teacher are wrong. The mean of the discrete random variable X is calculated as the sum of each value multiplied by its probability, which results in a mean of 3. The variance is calculated using the squared differences from the mean, leading to a variance of 2. Therefore, both the student's mean and the teacher's variance are incorrect.

A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean of X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true? k: 1 2 3 4 5 P(X=k): 0.1 0.2 0.4 0.2 0.1

Solution

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