Astronomers treat the number of stars in a given volume of space as a poisson random variable. the density in the milky way galaxy in the vicinity of our solar system is 1 star per 16 cubic light years. (a) what is the probability of 2 or more stars in 16 cubic light years? probability = . [round your answer to three decimal places (e. g. 98.765).] (b) how many cubic light years of space must be studied so that the probability of 1 or more stars exceeds 0.98? cubic light years of space. [round your answer to the nearest integer.]

a) 0.264 b) 64 cubic light years

Step-by-step explanation:

Let be X the following event : ''Number of stars in a given volume of space''

X~Poisson variable

X~P(k;λ)

The density is 1 star per 16 cubic light years so

λ = 1 star / 16 cubic light years

The probability mass function of X is :

f(x)= P(X = k) = {[(λt) ^ k].[(e) ^ (-λt)]} / k!   ;  k∈Νo

We measure t in units of 16 cubic light years

λt = (1 star / 16 cubic light years).(1).(16 cubic light years) = 1 star

a)

b) We are looking for t so that :

t≥3.912 ≈4

We should explore 4.16=  64 cubic light years of space to find a star with the certain of 98%.

19

step-by-step explanation:

6x = 48

i hope this . 6 cards each and a total of $48. dvide each side by 6 and you will have your answer.