Mean and standard deviation of a discrete random variable

Practice calculating and interpreting the mean and standard deviation of a discrete random variable.

Example: Ticket sales for a concert

Organizers of a concert are limiting tickets sales to a maximum of 44 tickets per customer. Let TT be the number of tickets purchased by a random customer. Here is the probability distribution of TT:
T=# of ticketsT= \# \text{ of tickets}11223344
P(T)P(T)0.10.10.30.30.20.20.40.4
Question 1
Calculate the expected value of TT.
μT=\mu_T=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
tickets

Question 2
Choose the best interpretation of the mean (or expected value) that you found in the previous question.
Choose 1 answer:
Choose 1 answer:

Question 3
Calculate the standard deviation of TT.
Round your answer to three decimal places.
σT=\sigma_T=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
tickets
For reference, here is the distribution again:
T=# of ticketsT= \# \text{ of tickets}11223344
P(T)P(T)0.10.10.30.30.20.20.40.4

What do you think is the best interpretation of the standard deviation that you found in the previous question?
Feel free to discuss this in the comments! Keep in mind that standard deviation describes how far away from the mean data points tend to fall.
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