Suppose that you have ten lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential distribution with parameter 3.

(a) What is the probability that all ten bulbs fail before time t?

(b) What is the probability that exactly k of the ten bulbs fail before time t?

(c) Suppose that nine of the bulbs have lifetimes that are exponentially distributed with parameter λ

and that the remaining bulb has a lifetime that is exponentially distributed with parameter θ (it is made by another manufacturer). What is the probability that exactly five of the ten bulbs fail before time t?

I'm kinda lost ! 1. when marilyn takes her pet dog for a walk, the dog walks at a veryconsistent pace of 0.55 m/s. draw a position-time graph to representmarilyn's dog walking the 19.8 m distance from the front of her house tothe nearest fire hydrant.2. both car a and car bleave school when a stopwatch reads zero. car atravels at a constant 75 km/h, and car b travels at a constant 85 km/h. a) draw a position-time graph showing the motion of both cars. howfar are the two cars from school when the stopwatch reads 2 hrs? calculate the distances and show them on your graph. b) both cars passed a gas station 120 km from the school. when dideach car pass the gas station? calculate the times and show themon your graph.3. the figure below shows the position-time graph showing a shopper'smovement up and down the aisle at a store. a) write a story describing the shopper's movements at the store. b) when does the shopper have a position of 6 m? c) how much time passes between when the shopper enters the aisleand when he gets to a position of 12 m? what is the shopper's averagevelocity between 37 s and 46 s?

Which articulations allow for greatest range of motion?

(1 point) match the differential equations and their vector valued function solutions. you may wish to multiply at least one solution out fully, to make sure that you know how to do it. you can get the other answers quickly by process of elimination and just multiply out one row element.