Calculus Applied to Probability and Statistics
by
Stefan Waner and Steven R. Costenoble

Answers to Exercises
for
Section 1: Continuous Random Variables and Histograms

1. Continuous Random Variables and Histograms 2. Probability Density Functions: Uniform, Exponential, Normal, and Beta Calculus and Probability Main Page "Real World" Page
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1. X is the number of the uppermost face; discrete.

3. X is the angle the pointer makes with the vertical; continuous with interval of values [0, 360).

5. X is the temperature at midday; continuous. There are many possible intervals of values, which depend on the scale of measurement being used (celcius, farenheit, or kelvin) and also what might be regarded as in the realm of possibility for a nidday temperature on earth. For instance, [150, 150] (degrees farenheit) might be reasonable on planet earth. However, (, +) would be incorrect no matter what units are used, since there is a lowest possible temperature (absolute zero, approximately -273.16 degrees celcius).

7. X is the U.S. Balance of Payments, rounded to the nearest billion dollars; discrete.

9. X is the number of computer chips that fail to work in a batch of 100; discrete.

11.

13.

15.
Age
0-15
15-25
25-35
35-45
45-55
55-65
65-75
75-95
Probability
0.2077
0.1199
0.1118
0.1443
0.1317
0.1317
0.0959
0.0570

(a) 0.5077(b) 0.5837 (c) 0.4163

17. (a) 0.304(b) 0.083 (c)0.237

19.

21. A random variable assigns a number to each outcome in an experiment.

23. It is half the corresponding area. of the heights of the corresponding bars on the 1-unit width histogram.

1. Continuous Random Variables and Histograms 2. Probability Density Functions: Uniform, Exponential, Normal, and Beta Calculus and Probability Main Page "Real World" Page
Return to Exercises

We would welcome comments and suggestions for improving this resource. Mail us at:
Stefan Waner (matszw@hofstra.edu) Steven R. Costenoble (matsrc@hofstra.edu)
Last Updated: September, 1996
Copyright © 1996 StefanWaner and Steven R. Costenoble