1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olya-2409 [2.1K]
3 years ago
5

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

d to be a very large number of planets that can be found this way, actually finding one takes time and luck; and finding one planet does not help at all with finding planets of other stars in the same part of the sky. Audrey is good at it, and finds one planet at a time, on average once every three months.
a.) Find the expected value and standard deviation of the number of planets she will find in the next two years.
b.) When she finds her sixth new planet, she will be eligible for a prize. Find the expected value and standard deviation of the amount of time until she is eligible for that prize.
c.) Find the probability that she will become eligible for that prize within one year.
Mathematics
1 answer:
Stolb23 [73]3 years ago
5 0

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%

You might be interested in
Jenny and her brother are arguing about who will get the larger peace of cake. They decided to have a coin toss. What is the pos
e-lub [12.9K]
The answer is 1/2 hope i helped
5 0
3 years ago
Read 2 more answers
HURRY WILL MAKE BRAINLEST!! circle F is shown below. EB is a diameter and the radius is 3 units. Choose the correct
Yuki888 [10]

Answer:

Arc length is equal to \theta r where \theta is the angle in radians and r is the radius.

Question 1:

\frac{\pi}{2}=\frac{\pi}{6}\times3

So the angle is CFD.

Question 2:

\pi=\frac{\pi}{3}\times3

So the angle is AFE.

Question 3:

2\pi=\frac{2\pi}{3}\times3

So the angle is AFB.

Question 4:

\frac{3\pi}{4}=\frac{\pi}{4}\times3

So the angle is BFC.

3 0
2 years ago
Help please !!!!!!!!!
Anni [7]

I’m not really sure about the answer but I’m doing the same think n this should help sorry ‍♀️

7 0
2 years ago
Read 2 more answers
Wrong answers only! + (Blank) = ​
zvonat [6]

Answer:

Step-by-step explanation:

1

6 0
3 years ago
Read 2 more answers
Simplify: power with a power 5^8*7^8
Rainbow [258]
Simplified the answer would b 35^8
3 0
3 years ago
Other questions:
  • Estimate by first rounding each number to the nearest . 1/2 3 4/11 2 1/10
    15·1 answer
  • Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M. How long did the movie last?
    11·1 answer
  • In what ways are products of fractions similar to products of integers?
    7·1 answer
  • −11b+7=40<br> solve for b
    13·2 answers
  • Which of the following sequences of numbers are arithmetic sequences?
    8·2 answers
  • What value of x will make the equation true? (√5) (√5)=x​
    9·1 answer
  • Simplify the product
    5·1 answer
  • What????????????????????
    8·1 answer
  • Help me ASAP bro this is hella weird
    6·2 answers
  • Expand the linear expression 6(7m+2)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!