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What does the mean of a discrete random variable represent?
What does the mean of a discrete random variable represent?
- The spread of the distribution
- The probability of each value
- The sum of all values
- The weighted average of possible values (correct)
In finding the mean of a discrete probability distribution, what is the first step?
In finding the mean of a discrete probability distribution, what is the first step?
- Calculate the sum of X * P(X)
- Subtract the computed mean from each value
- Construct the probability distribution (correct)
- Determine the value of X * P(X)
What does the variance of a discrete random variable measure?
What does the variance of a discrete random variable measure?
- The spread of the distribution
- The probability of the random variable
- The variability of the distribution (correct)
- The sum of all values
Which step is involved in finding the variance of a discrete probability distribution?
Which step is involved in finding the variance of a discrete probability distribution?
What does ∑(X - 𝝁)² * P(X) represent in the variance formula of a discrete probability distribution?
What does ∑(X - 𝝁)² * P(X) represent in the variance formula of a discrete probability distribution?
When finding the mean, what is multiplied by the corresponding probabilities?
When finding the mean, what is multiplied by the corresponding probabilities?
What is the formula for calculating the standard deviation of a probability distribution?
What is the formula for calculating the standard deviation of a probability distribution?
What is the purpose of Step 3 in finding the mean, variance, and standard deviation of a probability distribution?
What is the purpose of Step 3 in finding the mean, variance, and standard deviation of a probability distribution?
In Step 6 of calculating the probability distribution, what operation is performed on each result obtained in Step 5?
In Step 6 of calculating the probability distribution, what operation is performed on each result obtained in Step 5?
What is Step 8 primarily responsible for in the process of finding the standard deviation?
What is Step 8 primarily responsible for in the process of finding the standard deviation?
If 𝝈 = 0.866, what does this value represent in relation to the probability distribution?
If 𝝈 = 0.866, what does this value represent in relation to the probability distribution?
What does the standard deviation of a random variable measure?
What does the standard deviation of a random variable measure?
In the context of a discrete probability distribution, what does 𝜇 represent?
In the context of a discrete probability distribution, what does 𝜇 represent?
How is the variance calculated for a discrete random variable in this context?
How is the variance calculated for a discrete random variable in this context?
What is the formula to calculate the standard deviation for a discrete probability distribution?
What is the formula to calculate the standard deviation for a discrete probability distribution?
What does Step 7 in the process entail when calculating the variance?
What does Step 7 in the process entail when calculating the variance?
How can the standard deviation be obtained from the variance value?
How can the standard deviation be obtained from the variance value?
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Study Notes
Mean of a Discrete Probability Distribution
- The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take.
- Formula: 𝝁 = ∑ 𝑿 ∙ 𝑷(𝑿)
- Steps to find the mean:
- Construct the probability distribution for the random variable.
- Determine the value of 𝑿 ∙ 𝑷(𝑿)
- Add all the values of to 𝑿 ∙ 𝑷(𝑿) to determine ∑ 𝑿 ∙ 𝑷(𝑿)
Variance of a Discrete Probability Distribution
- The variance of a discrete random variable X measures the spread, or variability, of the distribution.
- Formula: 𝝈𝟐 = ∑(𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿)
- Steps to find the variance:
- Subtract the computed mean from each value of the random variable: 𝑿 − 𝝁
- Square the value obtained: (𝑿 − 𝝁)𝟐
- Multiply the value obtained by the given probability: (𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿)
- Find the variance by adding all products obtained
Standard Deviation of a Discrete Probability Distribution
- The standard deviation of a random variable measures how close the random variable is to the mean.
- Formula: 𝝈 = √∑(𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿)
- Steps to find the standard deviation:
- Find the variance: 𝝈𝟐 = ∑(𝑿 − 𝝁)𝟐 ∙ 𝑷(𝑿)
- Take the square root of the variance: 𝝈 = √𝝈𝟐
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