Question

A spinner marked off in seven ​equal-sized regions, numbered 1, 2, 3, 4, 5, 6, and 7​, is spun twice. Let the random variable X be the nonnegative difference between the numbers of the regions where the pointer​ stops, and define a probability mass function ​g(x)=​P(X=​x). ​a) State the range of X. ​b) Write g as a set of ordered pairs. ​c) Draw a probability distribution as a histogram. ​d) Find ​g(5​), and explain what this number represents. ​e) Find μ​, and explain what this number represents.

Answer 1

Step-by-step explanation:

To find - a) State the range of X. ​

              b) Write g as a set of ordered pairs.

              ​c) Draw a probability distribution as a histogram. ​

              d) Find ​g(5​), and explain what this number represents. ​

              e) Find μ​, and explain what this number represents.

Proof -

a.)

Range of X = { 0, 1, 2, 3, 4, 5, 6 }

b.)

(0, 7/49), (1, 12/49), (2, 10/49), (3, 8/49), (4, 6/49), (5, 4/49), (6, 2/49)

c.)

The graph is as follows :

d.)

The value of g(5) is 6/49

It represents the probability of the difference of the two spins is 5.

e.)

mean, μ = 2.29

It represents the average value of the spins