Answer to Question #254871 in Statistics and Probability for Clark

Question

1. Tasks/Questions: Observe the surroundings and try to create word problems involving Mean and Variance of Discrete Random Variable. For each problem you need to give illustration by using tables, diagrams or step by step procedure on how to answer the problem. See to it that the solution you provided is easy to understand. You can submit your work thru fb messenger or email. II. Expected Output: Formulate sample worksheet to represent problems involving Mean and Variance of Discrete Random Variable with solutions.

Answer 1

Example: Ticket sales for a concert

Organizers of a concert are limiting tickets sales to a maximum of 4 tickets per customer. Let T be the number of tickets purchased by a random customer. Here is the probability distribution of T:

T=# of tickets: 1 2 3 4

P(T): 0.1 0.3 0.2 0.4

the expected value (mean) of T:

$E(T)=\mu=\sum T_i P(T_i)=1\cdot0.1+2\cdot0.3+3\cdot0.2+4\cdot0.4=2.9$

the variance of T:

$Var(T)=\frac{\sum(T_1-\mu)^2}{n}=\frac{(1-2.9)^2+(2-2.9)^2+(3-2.9)^2+(4-2.9)^2}{4}=1.41$