Let the random variable X have the density function is given by (ex. Os xs5, fo)-1o, elsewhere. 1) The value of the constant C=; 2) The expected value of X is E(X)=; 3) The expected value of X2 is E(x²) 4) The variance of X is given by Var (X) =o? =.

Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.

Suppose that y, is an independent response variable (i = 1.....n) with mean, such that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3 is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pi) (Yi - Pi) + Ni w₁ = [V (pi) (g'(pi))²]-¹ 8 where g'(μ) = 9(μ) (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?

Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the expected value of Y. QUESTION 7 Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the variance of Y.

4. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.