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Questions and Answers
What is the formula used to calculate the mean of the probability distribution?
What is the formula used to calculate the mean of the probability distribution?
- $µ = ∑ 𝑋/𝑛$
- $µ = ∑ 𝑋𝑃(𝑥)/𝑛$
- $µ = ∑ 𝑋𝑃(𝑥)$ (correct)
- $µ = ∑ 𝑋^2𝑃(𝑥)$
What is the purpose of subtracting the mean from each value of the random variable $X$ in step 2?
What is the purpose of subtracting the mean from each value of the random variable $X$ in step 2?
- To calculate the variance
- To center the data around zero
- To calculate the standard deviation
- To find the difference between the values and the mean (correct)
Which step is used to calculate the variance of the probability distribution?
Which step is used to calculate the variance of the probability distribution?
- Step 4, where the results from step 3 are multiplied by the corresponding probability
- Step 5, where the sum of the results from step 4 is calculated
- Both steps 4 and 5 (correct)
- None of the above
What is the formula for calculating the variance of a probability distribution?
What is the formula for calculating the variance of a probability distribution?
What is the relationship between the variance and the standard deviation of a probability distribution?
What is the relationship between the variance and the standard deviation of a probability distribution?
What is the purpose of finding the sample mean in statistics?
What is the purpose of finding the sample mean in statistics?
What is the purpose of calculating the variance and standard deviation of a discrete probability distribution?
What is the purpose of calculating the variance and standard deviation of a discrete probability distribution?
What is the formula for calculating the variance of a discrete random variable $X$ with probabilities $p(x)$?
What is the formula for calculating the variance of a discrete random variable $X$ with probabilities $p(x)$?
If the mean of a discrete random variable is $\mu = 5$ and the variance is $\sigma^2 = 4$, what is the standard deviation?
If the mean of a discrete random variable is $\mu = 5$ and the variance is $\sigma^2 = 4$, what is the standard deviation?
The number of cars sold per day at a local car dealership has the following probability distribution:Number of Cars Sold (X): 0, 1, 2, 3, 4Probability (P(x)): 0.1, 0.2, 0.3, 0.2, 0.2What is the variance of this probability distribution?
The number of cars sold per day at a local car dealership has the following probability distribution:Number of Cars Sold (X): 0, 1, 2, 3, 4Probability (P(x)): 0.1, 0.2, 0.3, 0.2, 0.2What is the variance of this probability distribution?
If the sample mean of a set of data is $\bar{x} = 10$ and the sample standard deviation is $s = 3$, what is the sample variance?
If the sample mean of a set of data is $\bar{x} = 10$ and the sample standard deviation is $s = 3$, what is the sample variance?
What is the relationship between the variance and standard deviation of a random variable?
What is the relationship between the variance and standard deviation of a random variable?
What is the formula used to calculate the variance of the probability distribution?
What is the formula used to calculate the variance of the probability distribution?
What is the value of the standard deviation calculated from the given probability distribution?
What is the value of the standard deviation calculated from the given probability distribution?
What is the mean of the probability distribution for the number of heads when three coins are tossed?
What is the mean of the probability distribution for the number of heads when three coins are tossed?
Which of the following is the correct expression for the variance of the probability distribution?
Which of the following is the correct expression for the variance of the probability distribution?
What is the purpose of finding the variance and standard deviation of a probability distribution?
What is the purpose of finding the variance and standard deviation of a probability distribution?
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