The duration of a voice telephone call is an exponential random variable V with expected value E[V]=8 minutes, and the duration of data call is an exponential random variable D with expected value E[D] = d>8 minutes.

The null hypothesis is H0: a call is a voice call, while the alternative hypothesis is H1: a call is a data call.

The probability of a voice call is P[V]=0.8, while the probability of a data call is P[D]=0.2.

A binary hypothesis test measures T minutes, the duration of call. The decision is H0 if T≤t minutes. Otherwise, the decision is H1.

Write the formula for the false alarm probability as a function of t and d

An appliance store sells lamps at $95.00 for two. a department store sells similar lamps at 5 for $250.00. which store sells at a better rate

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.

Which equation is true? i. 56 ÷ 4·7 = 82 ÷ (11 + 5) ii. (24 ÷ 8 + 2)3 = (42 + 9)2 neither i nor ii ii only i and ii i only