Help !!!!!!!!!!!!!!!

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

Function 1: y = 4x + 5

rosijanka [135]

Answer:

Option B is correct

Function 1, because the slope is 4 and the slope of function 2 is 2.

Step-by-step explanation:

Slope-intercept form:

The equation of line is given by:

$y=mx+b$

where, m is the slope and b is the y-intercept

As per the statement:

Function 1: y = 4x + 5

On comparing with [1] we have;

Slope of function 1 = 4

Function 2: The line passing through the points (1, 6) and (3, 10).

Using slope formula:

$\text{Slope}= \frac{y_2-y_1}{x_2-x_1}$

Substitute the given points we have;

$\text{Slope}= \frac{10-6}{3-1}$

⇒ $\text{Slope}= \frac{4}{2}$

Simplify:

⇒ $\text{Slope}=2$

⇒ $\text{Slope}= \frac{4}{2}$

⇒ Slope of the function 2 is, 2

Since, function 1 is greater rate of change.( i.e 4 > 2)

Therefore,

Function 1 has the greater rate of change, because the slope is 4 and the slope of function 2 is 2.

3 0

3 years ago

Read 2 more answers

Cual es la utilidad de la representacion a escala de diferentes distancias reales

svp [43]

Answer:

Scales are used to represent real distances and proportions into maps and planes, that way we can have a bigger perspective about something just having in paper.

One direct use of scales are seen in architecture plans, there, the architect uses scales to represent the construction he is designing. Also, the architect can have a more complete point of view about the principial elements on his work.

6 0

3 years ago

KY wants to buy three shirts which were originally price 49.96 dollars eachhistorical discount the price of the third shirt and

shutvik [7]

Same question, c) 44.59

3 0

3 years ago

Read 2 more answers

Which of the following approaches would be an appropriate first step? select all that apply

Eva8 [605]

Answer:

Divide both sides by -1/3, Apply distributive property, add 1/3 to both sides

Step-by-step explanation:

If its confusing just replace -1/3 with a simple number such as -1, to make it make sense.

4 0

2 years ago