3g+h=18 2g+3h=26 what is g and what is h

According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Colorado" (J. of Water Res. Plann

mihalych1998 [28]

Answer:

(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.

6 0

3 years ago

The cleaning crew cleans 100 homes per week and earns a weekly economic profit of $200. the cleaning crew charges $80 per home.

loris [4]

$80(100) + $200 = $8200

8 0

3 years ago

Edward bought the 7 concert tickets for himself and 6 friends for a total of $168. Each friend paid Edward back for his or her t

levacccp [35]

Answer: $26

Step-by-step explanation:

Since the 7 tickets cost $168, the value of each ticket will then be:

= $168/7

= $24

Each ticket cost $24

If one friend gave him $50, the change that the friend will collect will be:

= $50 - $24

= $26

Therefore, Edward should return $26 to the person.

3 0

2 years ago

Solve for x 3x+1/2=4

Elden [556K]

The equation 3x+1/2=4

meaning x would equal 7/6

7 0

3 years ago

Read 2 more answers

PlzplPzlpzlzpzl .......i beg u do this easy question for me ....

jeka94

Answer: $-p^2-(q+r)^2$

Work Shown:

I'm assuming your teacher wants you to factor as much as possible.

$-p^2-q^2-r^2-2qr\\\\-p^2-q^2-2qr-r^2\\\\-p^2-(q^2+2qr+r^2)\\\\-p^2-(q+r)^2\\\\$

In the last step, I used the rule that $(a+b)^2 = a^2+2ab+b^2$

We cannot factor any further. If the first term was $p^2$ instead of $-p^2$ , then we could use the difference of squares factoring rule.

5 0

2 years ago