3. The random variable r represents the annual rainfall depth in El Paso in inches. Be- tween values of r = 0 and r = 15, the probability density function has the equation f(r) = 1 0
3. The random variable r represents the annual rainfall depth in El Paso in inches. Be- tween values of r = 0 and r = 15, the probability density function has the equation f(r) = 1 0
A First Course in Probability (10th Edition)
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![3. The random variable a represents the annual rainfall depth in El Paso in inches. Be-
tween values of r = 0 and r = 15, the probability density function has the equation
1
f(x) =
15
0<r< 15
(a) Sketch the complete PDF. Demonstrate that f f(r)dr = 1.0.
(b) Find the probability that next year's rainfall will not exceed 5 inches.
(c) Find the probability that annual rainfall will equal or exceed 10 inches for the
next three consecutive years.
(d) Calculate the mean value of annual rainfall using the expected value E[r] equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12ca14a1-de10-476a-942d-19b98bac76a3%2F4b1f4395-1a9d-487e-a486-c70ed7391747%2F5p51djj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. The random variable a represents the annual rainfall depth in El Paso in inches. Be-
tween values of r = 0 and r = 15, the probability density function has the equation
1
f(x) =
15
0<r< 15
(a) Sketch the complete PDF. Demonstrate that f f(r)dr = 1.0.
(b) Find the probability that next year's rainfall will not exceed 5 inches.
(c) Find the probability that annual rainfall will equal or exceed 10 inches for the
next three consecutive years.
(d) Calculate the mean value of annual rainfall using the expected value E[r] equation.
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