The states of Ohio, Iowa, and Idaho are often confused, probably because the names sound so similar. Each year, the State Tourism Directors of these three states drive to a meeting in one of the state capitals to discuss strategies for attracting tourists to their states so that the states will become better known. The location of the meeting is selected at random from the three state capitals. The shortest highway distance from Boise, Idaho to Columbus, Ohio passes through Des Moines, Iowa. The highway distance from Boise to Des Moines is 1350 miles, and the distance from Des Moines to Columbus is 650 miles. Let d1 represent the driving distance from Columbus to the meeting, with d2 and d3 representing the distances from Des Moines and Boise, respectively

a. Find the probability distribution of d1 and display it in a table.
b. What is the expected value of d1?
c. What is the value of the standard deviation of d1?
d. Consider the probability distributions of d2 and d3. Is either probability distribution the same as the probability distribution of d1? Justify your answer.
e. Define a new random variable t = d1 + d2. Find the probability distribution of t.

The driving distance for meeting at the three centres can be written as

d1=columbus

d2=Des moines

d3=Boise

The distance from des moines to columbus to 650 miles

from Boise to des moines is 1350

Therefore the distance from columbus to Boise

if the meeting is holding at columbus

0+650+1350=2000

Pr(columbus)=1/3

Pr(Des moines)=1/3

Pr(Boise)=1/3

a. Probability distribution is

capital       c            DM         B

di               0            650        2000

Pr(di)           1/3           1/3         1/3

b. Expected value is multiplication of the probability of d1 and the outcome

E(x)=0*1/3=0

c. find the variance of d1 first

Var=(x-E(x))^2*Pr(d1)

Var=(0-0)^2*1/3

Var=0

the square root of var=standard deviation

S.D=0

d. probability distribution of d2 and d3 is equal to the probability distribution of d1 , because they all have a probability of 1/3(the likelihood that an event will occur is 1/3 for the meeting \location

e. d1=0

d2=650

d1+d2=650

pr(d1+d2)=1/3+1/3=2/3

Pr(d1+d2) will be on the vertical axis, while d1+d2 will be plotted on the horizontal axis of the probability distribution graph

Step-by-step explanation:

The driving distance for meeting at the three centres can be written as

d1=columbus

d2=Des moines

d3=Boise

The distance from des moines to columbus to 650 miles

from Boise to des moines is 1350

Therefore the distance from columbus to Boise

if the meeting is holding at columbus

0+650+1350=2000

Pr(columbus)=1/3

Pr(Des moines)=1/3

Pr(Boise)=1/3

a. Probability distribution is

capital       c            DM         B

di               0            650        2000

Pr(di)           1/3           1/3         1/3

b. Expected value is multiplication of the probability of d1 and the outcome

E(x)=0*1/3=0

c. find the variance of d1 first

Var=(x-E(x))^2*Pr(d1)

Var=(0-0)^2*1/3

Var=0

the square root of var=standard deviation

S.D=0

d. probability distribution of d2 and d3 is equal to the probability distribution of d1 , because they all have a probability of 1/3(the likelihood that an event will occur is 1/3 for the meeting \location

e. d1=0

d2=650

d1+d2=650

pr(d1+d2)=1/3+1/3=2/3

Pr(d1+d2) will be on the vertical axis, while d1+d2 will be plotted on the horizontal axis of the probability distribution graph

step-by-step explanation:

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