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Statistics and Probability

Question and Answer:

1. What is the variance and standard deviation of a random variable?

• The variance is a measure variability. It is calculated by taking the average of squared deviations from the mean. The standard deviation is a measure of the amount of variation. It is calculated by taking square root of the variance.

2. What does the variance and standard deviation of a probabilty distributiou tells is?

• The variance and standard deviation of a probabilty distribution tells us the amount of spread, dispersion, or variability of the items in a distribution

3. How do you interpret the variance and standard deviation of a probabilty distribution?

• The larger the variance and standard deviation in relation to the mean, the more spread or disperse is the data.

What I Can Do:

The number of computers sold per day at a local computer store, along with its corresponding probabilities, is shown in the table. Find the variance and standard deviation of the distibution.

Solution:

Multiply value of the random variable x by the corresponding probability:

X • P(X)

Get the mean by getting the sum of X • P(X)

μ = ΣX • P(X)

μ = 0.0 + 0.2 + 0.6 + 0.6 + 0.8

Subtract the mean from each value of the random variable x:

X - μ

Square the results of X - μ

(X - μ)²

Multiply the results of (X - μ)² by the corresponding probability:

(X - μ)² • P(X)

Get the sum of the results in (X - μ)² • P(X) to get the variance:

Get the square root of the variance to get the standard deviation:

Answer:

The variance of the probabilty distribution is 16.40.

The standard deviation of the probabilty distribution is 4.05.

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