LetXbe a continuous random variable with densityf(x) ={3e−3x, whenx >0,0,elsewhere.(a) Verify thatfis a density function.(b) CalculateP(−1< X <1).(c) CalculateP(X <5).(d) CalculateP(2< X <4|X <5).(e) Find the cumulative distribution function ofX.(f) Find theEXandEe2X.(g) Find the variance ofX.

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

This is a map of the mars exploration rover opportunity predicted landing site on mars. the scale is 1cm : 9.4km. what are the approximate measures of the actual length and width of the ellipse? i mostly need to know how to set it up : )

Can someone explain to me how to do