given the following probability function for N: fN(n)={0.16 for n=0,0.42 for n=11,0.22 for n=35,0.08 for n=43, and 0.12 for n=54}. What is the expected value of N? Give your answer as a decimal.

What is the volume of the sphere shown below with a radius of 3?

Drag the tiles to the correct boxes to complete the pairs. using the properties of integer exponents, match each expression with the correct equivalent expression.

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?