Exercise 1. Exponential Random Variable is Memoryless. The time T until a new light bulb burns out is an exponential random variable with parameter λ. Jane turns the light on, leaves the room, and when she returns, t time units later, finds that the bulb is still on, which corresponds to the event A = {T > t}. Let X be the additional time until the bulb burns out. What is the conditional CDF of X, given the event A?

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

An object in geometry with no width, length or height is a(n):

The perimeter of an equilateral triangle is 4 cm more than the perimeter of a square and the length of a side of the triangle is 8 cm more than the length of a side of the aware. find the length of a side of the equilateral triangle