Let {x; t = 1,2, ...} be a covariance stationary process and define y, = Cov(x, x+h) for h = 0. [Therefore, yo = Var(x,).] Show that Corr(x, X1+h) = YWY0-

Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

A:

Q: Let 7'(t) = (3+ 4t, cos(t), 6e*) and F(0) = (7, 2, 5). Determine 7(t). †(t) = (, , )

A:

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: What is the value of the beta function, B(x, y), where x and y are positive real numbers?

A: We have to write the value of the beta function, B(x, y), where x and y are positive real numbers!

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

A:

Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Let f(x, y, z) = x³y5 + z4 and x = (a) Calculate the primary derivatives of, of of дх' ду'dz' (Use…

A:

Q: 3. The Cov(X) of a random vector X'= (X₁, ..., Xn) is defined as E{(X-E(X))'(X-E(X)}. True or false,…

A: We know that, X' is a vector and Covariance of a vector X is equal to the variance of X.  Which…

Q: Let X ~ Uniform(-1,1) and Y = X² , find the CDF and PDF.

A: Use the following definitions, to obtain the solution. The cumulative distribution function of a…

Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

A:

Q: 6. If f(x,y) = 2 x>0; y>0; x+y<1 Show the conditional pdf of Y given x is uniform.

A: