Question

Consider the continuous uniform distribution.

a. Why would you use this to model the distribution of ages of people between the ages of 0 and 50 years in the United States?

b. Why would this likely not be a good distribution to use beyond about 50 years of age?

c. Is this distribution characterized as a PMF or PDF? Explain.

d. What is the mean age? Show your calculation.

e. What is the standard deviation? Show your calculation.

f. What is the probability that a person will be exactly 30 years of age? Explain your answer.

g. What is the probability that a person will be between ages 30 and 31? Show your calculation.

Answer 1

The continuous uniform distribution is given by X~ U(A,B) with pdf = 1/ (b-a).

a) The continuous uniform distribution is used as the range, given with the lower limit as 0 and the upper range as 50.

X ~ U(0,50)

b) The distribution is not good to use beyond 50 years of age as after 50 years, the upper limit will be infinity.

c) The continuous uniform distribution is characterized as probability density function.

The discrete distribution gives probability mass function.

d) The mean for the continuous uniform distribution is given by (a+b)/2. That is, (0+50)/2 = 25.

e) The standard deviation of the continuous uniform distribution is given by square root value of (b-a)² / 12.

or, square root value of (50-0)² / 12. = 14.43.

f) The probability that the person is exactly 30 years old is zero, as at a particular point, the continuous distribution gives zero probability.

g) The probability that the person is between 30 and 31 years of age is calculated as:

$ = 1/ 50 = 0.02.