- ____ Suppose that XX followed the theoretical distributions below. Set up each distribution using the appropriate information from your data.
- ____ Uniform: X ~ UX ~ U ____________ Use the lowest and highest values as aa and bb.
- ____ Exponential: X ~ ExpX ~ Exp ____________Use
x¯
x
to estimate μμ .
- ____ Normal: X ~ NX ~ N ____________ Use
x¯
x
to estimate for μμ and ss to estimate for σσ.
- ____ Must your data fit one of the above distributions? Explain why or why not.
- ____ Could the data fit 2 or 3 of the above distributions (at the same time)? Explain.
- ____ Calculate the value k k (an XX value) that is 1.75 standard deviations above the sample mean.
k k = _________ (rounded to 2 decimal places) Note: k = x¯
+ (1.75)*sk=
x
+(1.75)*s
- ____ Determine the relative frequencies (RFRF) rounded to 4 decimal places.
- 1. RF = frequencytotal number surveyedRF=frequencytotal number surveyed
- 2. RF(X < k)RF(X<k) =
- 3. RF(X > k)RF(X>k) =
- 4. RF(X = k)RF(X=k) =
Use a separate piece of paper for EACH distribution (uniform, exponential, normal) to respond to the following questions.
You should have one page for the uniform, one page for the exponential, and one page for the normal
- ____ State the distribution: X X ~ _________
- ____ Draw a graph for each of the three theoretical distributions. Label the axes and mark them appropriately.
- ____ Find the following theoretical probabilities (rounded to 4 decimal places).
- 1. P(X < k ) P(X < k ) =
- 2. P(X > k ) P(X > k ) =
- 3. P(X = k )P(X = k ) =
- ____ Compare the relative frequencies to the corresponding probabilities. Are the values close?
- ____ Does it appear that the data fit the distribution well? Justify your answer by comparing the probabilities to the relative frequencies, and the histograms to the theoretical graphs.
(What does "Endorsed by" mean?)
"Reviewer's Comments: 'I recommend this book. Overall, the chapters are very readable and the material presented is consistent and appropriate for the course. A wide range of exercises introduces […]"