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 ?

Individual A has a red die and B has a green die (both fair). If they each roll until they obtain five "doubles" (1-1,...,6-6), what is the pmf of X (= the total number of times a die is rolled)? What are E(X) and V(X)?

Find the linearization at x = a. 1 f(x) = = 5 +3

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following. y P(y) 0 0.60 (a) Compute E(Y). E(Y) E 1 0.25 Need Help? Read It 2 0.10 3 0.05 (b) Suppose an individual with y violations incurs a surcharge of $110Y2. Calculate the expected amount of the surcharge. $

Let f(x) = x2 g(x) = 2x-3 h(x) = Vx+1 %3D %3D 5. (g o f)(1) 6. (h o g)(5) 7. (g oh)(1) 8. (fo g)(x)

A research center claims that 28% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 31% say that they would travel into space on a commercial flight if they could afford it. At x = 0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. At least % of adults in the country would travel into space on a commercial flight if they could afford it. B. No more than % of adults in the country would travel into space on a commercial flight if they could afford it. C. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not % of adults in the country would travel into space…

If T(x)be an estimator of 0, then bias term can be defined as, 0- E[T(x)] E[T(x)]=® E[T(x)]-®² a) b) c) d) T(x)-0

If f(x) = a* + 2, g(æ) = x – 7 and h(x) = Va, then f(g(h(x)))= Preview

Let X- B(25,0.2). E(X²) =

(a) Sx* d(x³). Note a(x) = x³. 3