Let there be a pair of rabbits. For the purpose of this exercise, the following assumptions are made.
Rabbits take one month to reach an age at which they may give birth.
Every month thereafter, a breeding pair of rabbits produce one further pair of rabbits.
Rabbits never die and never stop being able to produce further rabbits.
How many pairs of rabbits will be produced from this single pair of rabbits after one year?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Multiply and simplify. 2x^2 y^3 z^2 · 4xy^4 x^2 i will mark you brainliest if right. show how you got the answer, !

Proving the congruent supplements theorem