B. Mills works as a construction worker. He makes a salary of 54,200 a year. After
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Answer and Explanation:
Given : The random variable x has the following probability distribution.
To find :
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.
Solution :
First we create the table as per requirements,
x P(x) xP(x) x² x²P(x)
0 0.25 0 0 0
1 0.20 0.20 1 0.20
2 0.15 0.3 4 0.6
3 0.30 0.9 9 2.7
4 0.10 0.4 16 1.6
∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1
a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.
Yes it is a probability distribution.
b) The expected value of x is defined as
c) The variance of x is defined as
d) The standard deviation of x is defined as
Consider the attached tree.
You start from the root, and with each level you create a sub-branch for each of the choices you have.
So, the root has two children, white and multigrain bread.
Each of those children has three children, because you have three meat choices
Each of those children has two children, because you have two cheese choices.
Then, you identify all the sandwiches by choosing a leaf, and read the label that lead you there.
For example, leaf number 4 represents a sandwich with white bread, turkey and provolone.
