Need help with last two questions, please!
XUni(-1,),Y-X + c,c > 0, what is P(Y -cl< 0.5) X ~ Uni(-1,1), Y = X + c, c > 0, what (a function ...
The answer I got was A = c -
.1. But this answer does not make sense to me, because how can Y -
0.9 < c < c - .1? If this is the correct answer, please give
an explanation of why the answer makes sense as well. Thank
you!
X ~ Uni(-1,1), y-X+ c, c 0, what (a function of Y) can we replace the "A" mark so that the PY-0.9 〈 c 〈 "A") = 0.9
X...
1. Let X and Y have a discrete joint distribution with ( P(X = x, Y = y) = {1, 10, if (x, y) = (-1,1) if x = y = 0 elsewhere Show that X and Y are uncorrelated but not independent. [5 points] 2. Let X and Y have a discrete joint distribution with f(-1,0) = 0, f(-1,1) = 1/4, f(0,0) = 1/6, f(0, 1) = 0, $(1,0) = 1/12, f(1,1) = 1/2. Show that (a) the two...
1. (10 points) The joint probability mass function of X and Y is given by p(1,1)= P(2,1)= 0, P(3,1) = 2 P(1, 2) = 1 p(2, 2) = 2 P(3, 2) = 16 p(1,3) = (2, 3) = 0, P(3, 3) = 5 Find (a) PX\Y(3,1); (b) E[X Y = 2) and (c) Fyx (2/1).
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
10. Let X and Y have a discrete joint distribution with if (x,y) = (-1,1) P(X = 2, Y = y) = { = ; if x=y=0 = 0, elsewhere Find (a) the conditional distribution of Y given X = -1. (b) show that X and Y are uncorrelated but not independent. (C) Find the marginal distributions of X and Y.
The Heaviside step function is a mathematical function defined by h(x) := ( 1 : x ≥ 0 0 : x < 0 that is to say, h(x) is 1 for non-negative x and 0 for negative x. In this question we will prove that the following code computes h(x) if (x >= 0): y = 1 else: y = 0 a) Define a predicate p(x, y), written solely in terms of logical ANDs and ORs, inequalities and equalities, which...
Curve Sketching: Use the following guidelines to sketch the graph of y-f(x) x-5x (20 points) a. What are the behaviors of y when x->oo, or x--0? (3 points) b. What is the first derivative of this function? What are increasing intervals and decreasing intervals and max points and mini points? (6 points) c. What are the second derivative of this function? What are intervals for concavity upwards and concavity downwards and inflection points? (6 points) Use the above information (a,...
Suppose that f(x) =1.5x2 for -1 < x < 1. What is P(0<x)? For the function listed above, what is P(-0.5< X < 0.5)? Still using the function above, what is P(X<-3)?
Evaluate the line integral of the function f(x,y)= (x+y2)/(sqrt(1+x2)) over the curve C: y=x^2/2 ; from (1,1/2) to (0,0)
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2 and f(x.y) = 0 3. otherwise. (a) Show that f(xy) is a density function. (b) Find the probability that both X and Y are less than one. (c) Find the marginal densities of X and Y and show that they are not independent. (d) Find the conditional density of X given Y when Y = 0.5.