Xn = a sin(bn + Z), n = Z, where a and b are positive constants and Z is a random variable with uniform distribution on the interval [-,]. Show that X₁ is a stationary sequence.
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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.Simplify the likelihood ratio e (µ1,..., Hr, o2) max (µ1,...,Hr,o²)EO0 e (41,...,Hr; o2) ' max (41,...,Hr,0²)EO SSTR/(r-1) SSE/(nt-r) and show that A is a decreasing function of F =
- (3) Let X = b >(8,-) find E(5+6x) and distribution function.show that 1-2% show that B(wn) p(ntt, n+t) =표산에.The X be a continuous random variable with cumulative distribution function 1 F(x) = 1 for x > 0 (and zero otherwise). - 1+ x Find the cumulative distribution function of Y = log X and sketch its curve.
- Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. Find the probability that the patient would die before receiving transplant.Let X be a continuous random variable whose moment generating function is 4x(t) = (5) ³. Find Var (X)Let random variable X be uniform in the interval (0, 1). Define random variable Y = aX + b where a not 0.
- Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.(13) Let X b(6,-) find E(5+6x) and distribution function. 3The time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let T1 and T2 be two independent waiting times for this distribution. Find expected time between each call and variance. (E(T) and V(T)) Find the probability for both T1 and T2 to be greater than one.