Here,
and
So, 2X + Y ~ Normal( 3, 52)
Also,
and
So, 4X - 2Y ~ Normal(2, 102)
Now,
(ans)
Suppose X, Y are independent and X~N(1,4) and Y N(1,9). If P(2X Y a) P(4X -...
2. Suppose that X1, ..., Xd N(0,9) and suppose that Y1, ..., Y10 d (1,9). Assume that all the Xs and Ys are independent of one another. (a) Determine the distributions of X and Y. (b) Determine the distribution of X1/Sy. (c) Compute P(S< 2.393). (d) Find an interval (a, b) such that Pla < s <b) = 0.95. Make the interval such that s has equal probability of being below a as of being above b. (e) Determine the...
Suppose X ~N(0,9) and Y ~N(1,16) X and Y are independent, then P(0<X+Y<2) =
1. Let X.. xs ^ N(-1,4) and Y.. y, " N(0.1) be independent. Using properties of the normal distribution, derive the distribution of the following random variables (b) Wa = 2.1(X + 1)
probability course 01) 6 and Let X and Y be two independent random variables. Suppose that we know Var(2X-Y) Var(X+ 2Y) 9, Find Var(X) and Var(Y).
2.) y = 2x² +10 with parabola y = 4x +16. x = -2 and x = 5 Find the area of the region bounded by the lines.
Let V be the set of vectors [2x − 3y, x + 2y, −y, 4x] with x, y R2. Addition and scalar multiplication are defined in the same way as on vectors. Prove that V is a vector space. Also, point out a basis of it.
Suppose X and Y are independent Binomial random variables, each with n=3 and p=9/10. a. Find the probability that X and Y are equal, i.e., find P(X=Y). b. Find the probability that X is strictly larger than Y, i.e., find P(X>Y). c. Find the probability that Y is strictly larger than X, i.e., find P(Y>X).
Determine the quadratic function whose graph is given. 16) +++++++++ ++++++ + Vertex: (-1,9) y-intercept: (0,8) A) f(x) = -x2 - 2x + 8 C)f(x) = -x2 - 2x - 8 B) f(x)=x2 - 4x + 8 D) f(x) = -x2 - 4x + 8
p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0 p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0
Problem 25 please -Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e 22. W= Span(B),where B= ({x25, x5*, 5x)); f(x)--4x2 5x+9s5x-2(5x). 3 W Span(B), where B (Exsin(2x), xcos(2x), sin(2x), cos(2x)y): f(x) = 4x sin(2x) + 9x cos(20-5 sin(2x) + 8 cos(2x). 24, In Exercise 21 of Section 3.6, we constructed the matrix [D, of the derivative operator D on W- Span(B), where B e sin(bx), e" cos(bx)): Dls a a. Find [D 1g and [D'lg: Observe...