What is the place value for 4 in 12354897

Audrey, an astronomer is searching for extra-solar planets using the technique of relativistic lensing. Though there are believe

Stolb23 [73]

Answer:

Step-by-step explanation:

The model $N (t)$ , the number of planets found up to time $t$ , as a Poisson process. So, the $N (t)$ has distribution of Poison distribution with parameter $(\lambda t)$

a)

The mean for a month is, $\lambda = \frac{1}{3}$ per month

$E[N(t)]= \lambda t\\\\=\frac{1}{3}(24)\\\\=8$

(Here. t = 24)

For Poisson process mean and variance are same,

$Var[N (t)]= Var[N(24)]\\= E [N (24)]\\=8$

(Poisson distribution mean and variance equal)

The standard deviation of the number of planets is,

$\sigma( 24 )] =\sqrt{Var[ N(24)]}=\sqrt{8}= 2.828$

b)

For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter $\lambda$ . The sum of $K$ of these independent exponential has distribution Gamma $(K, \lambda)$ .

From the given information, $k = 6$ and $\lambda =\frac{1}{3}$

Calculate the expected value.

$E(x)=\frac{\alpha}{\beta}\\\\=\frac{K}{\lambda}\\\\=\frac{6}{\frac{1}{3}}\\\\=18$

(Here, $\alpha =k$ and $\beta=\lambda$ )

C)

Calculate the probability that she will become eligible for the prize within one year.

Here, 1 year is equal to 12 months.

P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)

$=\frac{1}{Г (6)(\frac{1}{3})^6}(12)^{6-1}e^{-36}\\\\=0.2148696\\=0.2419\\=21.49%$

Hence, the required probability is 0.2149 or 21.49%

5 0

3 years ago

3(n-4)=5n+4<br><br> What does n equal?

Angelina_Jolie [31]

Your answer is n=2. thank me if this helped you. :)

7 0

3 years ago

Solving a right triangle (round to the nearest tenth)

Inga [223]

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180 for A

A = 180° - (90 + 46)° = 180° - 136° = 44°

----------------------------------------------------------------

tan46° = $\frac{opposite}{adjacent}$ = $\frac{b}{23}$

Multiply both sides by 23

23 × tan46° = b, thus

b ≈ 23.8 ( to the nearest tenth )

-----------------------------------------------------------------

cos46° = $\frac{adjacent}{hypotenuse}$ = $\frac{23}{c}$

Multiply both sides by c

c × cos46° = 23 ( divide both sides by cos46° )

c = $\frac{23}{cos46}$ ≈ 33.1 ( to the nearest tenth )

5 0

3 years ago

The sun produces 3.8x10^27 joules of energy per second. How much energy is produced in a year? (Note: a year is approximately 31

Slav-nsk [51]

About 1.204972095x10^20 joules in a year

3 0

3 years ago

3x²-4x+7 how do I find the domain?

Eddi Din [679]

The domain of this equation is the lowest x value to the highest x value. For example: lowest is -4 and highest is 3. You would write it as [-4,3]

For this equation, the domain is (-infinity,infinity) because there is no lowest or highest x value.

8 0

3 years ago