In order for a discrete random variable to be modeled as binomial, what must be true about the random process/experiment that generates the values for the random variable?

The correct answer is the random experiment must be done via a bernoulli process.

Step-by-step explanation:

Binomial distribution gives the number of successes in n independent experiments, all being a bernoulli trial. Bernoulli distribution can be considered as a particular case of binomial distribution where n = 1. Bernoulli experiment is a success-failure or boolean type experiment or the probability is equal for every value of random experiment.

Thus in order for a discrete random variable to be modeled as binomial, the process should be bernoulli with equal probabilities for every random variable.

b.an increase in a causes b to decrease

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3