Let (W)to be a Brownian Motion. We consider the stochastic process (X+)+20 defined by X₁ == [wds. W, ds. (a) Find E[X] and Var(X+). (Use the properties of Brownian Motion seen in class.) (b) Give an argument (it doesn't have to be rigorous) explaining why X has normal distribution. (c) Is (X) a martingale ?

Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

(21) Let X b(12,–) find E(5+6x) and distribution function.

3. Consider this function: g(x) = (x - 273) + 32 . (a) Determine the function which will 'undo' everything this original equation does. All work must be shown! tool.] (b) Describe a way you could "test" your equation in part (a) to see if it truly will 'undo' the original function. [ (c) The original equation is not random! That given equation will convert from a = a known temperature in degrees Kelvin into g(x) =equivalent temperature in degrees Fahrenheit.