3. Let y be distributed as N3 (μ, E) where (-²¹). 2 1 0 1 1 1 4. μ = Σ =|1 0 Find the distribution of z = 2y₁ - y3 + 3y2.

Q: held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with o…

A: Sample size n =100 Sample mean=58.3 Population standard deviation =3

Q: 9. If Y is distributed chi-square with 8 degrees of freedom. x²(9), find: e) K a value of y such…

A:

Q: 4. Suppose Y1, Y2 are independently and identically distributed with Unif((0,1)). Let Z = Y1 · Y2…

A:

Q: Let Y have a gamma distribution with parameters a and 3, so that the pdf of Y is fy(y) =…

A: The PDF of Y is given as:

Q: 4. Find the expected values of ry 5. find the covariance Cov(X,Y) 6. find the correlation Cor(X,Y)

A: Expected value of xy: The expected value of xy can be calculated as: E[xy] = ∫∫ xy * f(x, y) dx dy…

Q: 5. A statistical model for the data y = (y1,.. (Y1,, y8) is a random sample from normal distribution…

A: The text in the image specifies the following:Data y = (y1, ..., yn) is a random sample from a…

Q: If X has a uniform distribution U(0, 1), find the pdf of Y = ex with ndf

A:

Q: Consider a mixture of two Gaussian distributions, [8.4 2 AN([12]. [6 %]) + 0.6N([8] · [²2* 1.7])…

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Q: Set n > 2. Let X1, X2, ..., Xn denote a random sample from a uniform distribution on (0, 1) i.e.…

A: Given that,  Xi ~U(0, 1) i= 1,2,3......n We have to find E(R) where R=Y(n) - Y(1)

Q: Suppose Y (Y1, Y2, Y3)' ~ N(u, Σ) where (a) (b) = -6 2 fl= and Σ Find the distribution of = [2 130 1…

A: The vector =(Y1, Y2, Y3)' ~N

Q: X = √-2 log U cos(2πV), Find the joint distribution of X and Y. (Hint: you may want to first compute…

A:

Q: Let X, denote the mean of a random sample of size n from a Gamma(, 1) distribution. Show that Vn (X,…

A:

Q: Let X and Y be normally distributed with X ~ N (14,a²) and Y ~ N(22,a²), a > 0. 5a. Find b so that P…

A:

Q: Q5. A continuous r.v. X is said to have a Gamma (a, B) distribution if its moment generating…

A:

Q: 9. Let Y1, Y2,., Yn denote a random sample from the probability density function given by 0-1 0<y<3…

A: Solution:- Given that pdf of y f(yθ) = θ yθ-13θ , 0 ≤y≤30 , elsewhere

Q: Q10 Suppose N ~ Poisson(10), and Y N = n ~ Binomial(n, p), for n = 0, 1, 2, . ... Q10(i.) Find the…

A:

Q: Find the distribution name and parameters for U=Y1+Y2 in each of these two cases with transformation…

A: The transformation formula for the sum of the two random variables is      fUu=∫-∞∞fY1,Y2u-y2, y2dy2…

Q: Find the mar gin al distribution of X. Find the margin al distribution of Y. Are X and Y…

A: For the independence of two variable X and Y, we must have f(x, y) = f(x).f(y)

Q: iid *1. Let Y₁,..., Yn uniform(0, 1). Find the distribution of their geometric mean: U = (ÎIx.)* ΠΥ…

A:

Q: Suppose the distribution of Y, conditional on X = x, is normal N(x, x) and that the marginal…

A: Given: The distribution of Y. conditional on X=x is, N(x,x²)

Q: Let X - U(1,3) with the following given PDF { ( 0.5, 1 <x < 3 f(x) = 0, EW Then, the variance of X…

A:

Q: 32. Suppose (X,Y, Z)' is normal with density C. exp{-(4r + 3y? + 522 +2ry +6rz+ 4zy) Azy)}. where C…

A:

Q: Let Yi < Y2 < ·.. < Y, be the order statistics of a random sample from a distribution with pdf f(1)…

A:

Q: 6. Let X1) be the minimum value in a sample of n independent observations from the distribution with…

A: Pdf of first order Statistic is  f(x) =n[1-F(x)]^(n-1) f(x)