What is sine times secant

At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable X as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

7 0

3 years ago

Consider the following scenario: Let P(C) = 0.4. Let P(D) = 0.5. Let P(C|D) = 0.6. a. Find P(C AND D). b. Are C and D mutually e

Nataly_w [17]

a. By definition of conditional probability,

P(C | D) = P(C and D) / P(D) ==> P(C and D) = 0.3

b. C and D are mutually exclusive if P(C and D) = 0, but this is clearly not the case, so no.

c. C and D are independent if P(C and D) = P(C) P(D). But P(C) P(D) = 0.2 ≠ 0.3, so no.

d. Using the inclusion/exclusion principle, we have

P(C or D) = P(C) + P(D) - P(C and D) ==> P(C or D) = 0.6

e. Using the definition of conditional probability again, we have

P(D | C) = P(C and D) / P(C) ==> P(D | C) = 0.75

3 0

3 years ago

Can someone do these 10 questions for me you only have to choose the correct letter please

Sergio039 [100]

I WOULD BUT I DONT KNOW!

6 0

3 years ago

Find two points on the line to be graphed. y-5=0

Nonamiya [84]

Any point with the y of 5 could be the answer

3 0

3 years ago

Does anyone know what the code is Ive been stuck on this for like ever.

timama [110]

Answer:

Binary code

Step-by-step explanation:

Code is a word or a symbol which is not disclosed to everyone and is considered as secretive. There are various codes which are required to run a software in order to minimize the risk of piracy. These codes are binary codes or java codes. These are complex so that not everyone can crack it.

3 0

3 years ago