Problem 1.

In Figure 1 are shown histograms of 6 simulated data sets. Below are the 6 distributions from which these data sets are simulated, but rearranged in a random order. Match the distribution to the histogram.

(A)

Uniform on [0,5].
Solution: Data set 6 has a range from 0 to 5 and the density looks pretty ``flat.''

(B)

Normal with mean 20 and standard deviation 5.
Solution: Data set 2 has a bell shape look centered at about 20.

(C)

Normal with mean 100 and standard deviation 25.
Solution: Data set 4.

(D)

Exponential with mean 20.
Solution: Data set 1 has the exponential look.

(E)

Weibull with parameters $\alpha = 2$ and $\beta = 20$.
Solution: Data set 3 is skewed right like a Weibull.

(F)

None of the above.
Solution: Data set 5 by a process of elimination.

  

Figure 1: Six histograms for Problem 1.