Choose the family of distributions that best fits the described situation: You want to model the number of lines of code run until the first 'bug' is detected. The probability a line of code has a bug is 0.003 or 0.3%.

Answer is : Geometric distribution

Let X be the number of lines of codes run until the first bug is detected

That is X is the random variable which is the number of trials needed to get first success. Success here is detection of bug . Success has constant probability in each trail which is p= 0.003 . That is before the first success we have    X-1 failures with probability (1-0.003)

The probability mass function of X is

P(X=x) = (1-p)x-1 p

P(X=x ) = (1-0.003)x-1 *0.003 , x= 1,2,

This distribution is also Negative Binomial distribution  

As geometric distribution is special case of Negative Binomial Distribution

In Negative Binomial distribution , we have r success ( r\geq 1) and the random variable is the number of Bernouli trials needed to get r successes .

If we put , r= 1, that is number of success is 1

Then the given situation , that is number of lines code run(X) before the first bug follow negative binomial distribution

The probability mass function of Negative Binomial distribution is

P(X=x) = (1-p)x-r pr ,x= r , r+1 ,

The probability mass function of X is

P(X=x, r=1 ) = (1-0.003)x-1 *0.003 , x= 1,2,

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.