Question

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A bag contains 8 numbered table tennis balls inside. Two balls are numbered 1, three are numbered 2, and three are numbered 3. Let the discrete random variable X = "number on a table tennis ball."
What are the expected value, variance, and standard deviation?

Answer 1

From the given discrete distribution, we have that:

$\mu = 2.13, \sigma^2 = 0.61, \sigma = 0.78$

What are the mean, the variance and the standard deviation of a discrete distribution?

• The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

• The variance is given by the sum of the difference squared between each observation and the mean, divided by the number of values.

• The standard deviation is the square root of the variance.

In this problem, the distribution is:

$P(X = 1) = \frac{2}{8}$

$P(X = 2) = \frac{3}{8}$

$P(X = 3) = \frac{3}{8}$

Hence, the mean is:

$\mu = 1\frac{2}{8} + 2\frac{3}{8} + 3\frac{3}{8} = \frac{17}{8} = 2.13$

The variance is:

$\sigma^2 = (1-2.13)^2\frac{2}{8} + (2-2.13)^2\frac{3}{8} + (3-2.13)^2\frac{3}{8} = 0.61$

The standard deviation is:

$\sigma = \sqrt{0.61} = 0.78$

More can be learned about discrete distributions at https://brainly.com/question/24855677