Question

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

as discussed in a previous problem

expected value = \[\sum_{}^{}x*P(x)\]

Answer 2

variance:

\[\sum_{}^{}x^{2}*P(x)-E^{2}\]
this calculation is very similar to the expected value calculation. however, instead of just multiplying (value) * probability, you square the value first, then multiply by its probability. then sum across all values.

after that, subtract the square of the expected value

Answer 3

standard deviation = sqrt(variance)

reference: https://www.mathsisfun.com/data/random-variables-mean-variance.html

Answer 4

Okay! Thank you so much!