Mathematics, 07.03.2020 04:53 kenyatte97

According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Colorado" (J. of Water Res. Planning and Mgmnt., 2005: 383–393), the drought length Y is the number of consecutive time intervals in which the water sup- ply remains below a critical value yo (a deficit), pre- ceded by and followed by periods in which the supply exceeds this critical value (a surplus). The cited paper proposes a geometric distribution with p = .409 for this random variable.

a. What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?

b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

Answers: 1

Show answers

Answers

Answer from: gonzalesnik

(a) P (Y = 3) = 0.0844, P (Y ≤ 3) = 0.8780

(b) The probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

Step-by-step explanation:

The random variable Y is defined as the number of consecutive time intervals in which the water supply remains below a critical value y₀.

The random variable Y follows a Geometric distribution with parameter p = 0.409.

The probability mass function of a Geometric distribution is:

$P(Y=y)=(1-p)^{y}p;\ y=0,12...$

(a)

Compute the probability that a drought lasts exactly 3 intervals as follows:

$P(Y=3)=(1-0.409)^{3}\times 0.409=0.0844279\approx0.0844$

Thus, the probability that a drought lasts exactly 3 intervals is 0.0844.

Compute the probability that a drought lasts at most 3 intervals as follows:

P (Y ≤ 3) = P (Y = 0) + P (Y = 1) + P (Y = 2) + P (Y = 3)

$=(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409+(1-0.409)^{2}\times 0.409\\+(1-0.409)^{3}\times 0.409\\=0.409+0.2417+0.1429+0.0844\\=0.8780$

Thus, the probability that a drought lasts at most 3 intervals is 0.8780.

(b)

Compute the mean of the random variable Y as follows:

$\mu=\frac{1-p}{p}=\frac{1-0.409}{0.409}=1.445$

Compute the standard deviation of the random variable Y as follows:

$\sigma=\sqrt{\frac{1-p}{p^{2}}}=\sqrt{\frac{1-0.409}{(0.409)^{2}}}=1.88$

The probability that the length of a drought exceeds its mean value by at least one standard deviation is:

P (Y ≥ μ + σ) = P (Y ≥ 1.445 + 1.88)

= P (Y ≥ 3.325)

= P (Y ≥ 3)

= 1 - P (Y < 3)

= 1 - P (X = 0) - P (X = 1) - P (X = 2)

$=1-[(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409\\+(1-0.409)^{2}\times 0.409]\\=1-[0.409+0.2417+0.1429]\\=0.2064$

Thus, the probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

Answer from: Quest

answer: the answer is c.

step-by-step explanation:

she’s dividing 1/3 of the flour into 2 jars.

hope this : )

Use the expression at the top right to answer the question (1/3 divided by 2)

Answer from: Quest

answer: input the dimensions of the room to be painted. click the button to calculate the amount of paint and man-hours needed for this job.

interior paint coverage depends on the brand of paint used. the coverage amount is listed on the label of the paint can. use this to adjust the values in the paint coverage section below. paint usually is applied at 350 to 400 square feet per gallon (primer at 200 to 300 square feet per gallon).

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:30, christinaS7696

First to answer all gets a donation question 3(multiple choice worth 1 points) (04.01 lc) which of the following levels is lower than cells in the hierarchy of organization of living things? molecules organs organ systems tissues question 4(multiple choice worth 1 points) (04.01 lc) which of these represents an individual form of life such as an animal, plant, or single-celled life form? organ organism organ system tissue question 5(multiple choice worth 1 points) (04.03 lc) what are the green structures inside plant cells where photosynthesis takes place called? chloroplast mitochondrion nucleus vacuole question 6(multiple choice worth 1 points) (04.03 lc) which of the following best matches a part of a living cell with the function it performs? cytoplasm: fluid which carries the nucleus and other organelles vacuole: fluid which carries the nucleus and other organelles cytoplasm: directs all of the cell's activities vacuole: directs all of the cell's activities question 7(multiple choice worth 1 points) (04.03 mc) read the table below. organelles of plant cells present in both plants and animals present in plants but not animals small in animals but large in plants organelle a organelle b organelle c which statement is most likely correct? organelle a is chloroplast, organelle b is cytoplasm, and organelle c is nucleus. organelle a is mitochondrion, organelle b is cytoplasm, and organelle c is nucleus. organelle a is cell wall, organelle b is chloroplast, and organelle c is mitochondrion. organelle a is mitochondrion, organelle b is chloroplast, and organelle c is vacuole. question 8(multiple choice worth 1 points) (04.03 mc) what will most likely happen in the absence of a nucleus? genetic information will not be transmitted by the cell. energy will not be released during cellular respiration. the cell will not store food, water, nutrients, and waste. the cell will lose its shape and structure.

Answers: 1

continue

Mathematics, 21.06.2019 20:30, nathanscastr02

The graph of y x3 is translated so that the point (1. 1) is moved to (1, 4). what is the equation of the new graph?

Answers: 1

continue

Mathematics, 21.06.2019 23:00, Kira4585

Divide. –4.2 ÷ 6 = a –0.7 b 0.7 c –7 d 7 me

Answers: 2

continue

Mathematics, 22.06.2019 00:00, xXwolfieplayzXx

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?

Answers: 3

continue

You know the right answer?

According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Color...