3. Given the joint density function 1(1+3y") 0< r < 2, 0< y < 1, f(r, y) = elsewhere, find g(x), h(y), f(xly), and evaluate P ( 1/4 < x < 1/2 | Y = 1/3).

Q: 5)? a What is P(Y₁ b What is P(Y₁+ Y₂ < 3)?

A:

Q: (3) Consider two variables Y₁, Y₂ whose joint probability density func- tion is given by 3y₁ if 0 ≤…

A: a) To find the marginal density f1(y1) of Y1, we need to integrate the joint density function…

Q: 3. Determine the constant a so that f(x) is a valid density function. - f(x) = {a(3 — x²), a) 0.3333…

A: Ans#- Given, f(x) is valid density function           f(x) = a(3 - x2)-1 ≤x≤10otherwise…

Q: 4. Given joint density f(x, y) = 1/y, 0 < x < y < 1, compute a) g(x) and h (y), b) P(X <= 1/4 , Y <=…

A: Given joint density function is: fx,y=1y; 0&lt;x&lt;y&lt;1 a). The g(x) and h(y):…

Q: Which of the following functions are continuous? 0. .(x, y) =(0,0) f(x,y) ={ 2x(x² – y²) I) (x, y) =…

A:

Q: )Suppose X is continuously uniformly distributed on [1, 4]. Let Y = ln(X). What is the density…

A: X~Uniform[1,4]

Q: The joint pdf of X and Y is given by fx,y(x,y) = {4x2   0<y<x<1}…

A: ANSWER: To determine the basis of a random variable U, we need to find the range of values ​​that U…

Q: 4. The joint density function of X and Y is given by if 0 < x < 1,0 <y < x? f(1,y) = othereise.…

A:

Q: The joint pdf of X and Y is given by fx,y(x,y) = {4x2   0<y<x<1}…

A: Sol:- To find the support of U, we first need to find the range of values that U can take

Q: Let X and Y have joint density f(x,y) = { 8(x + y²), 0≤x≤ 1,0 ≤ y ≤1 0, otherwise. Determine the…

A: We have to find  for the joint density function

Q: Inx 2) Find the average value of the function g(x) = over the interval [1, e].

A: Given the function g(x)=lnxx over the intercal [1, e].

Q: Given the joint density function f(x, y) = {"(1+3y2) 4 ,0 < x < 2,0 < y < 1 Ootherwise. Find the

A:

Q: Find the marginal densities of X and Y using the joint density fxy(x, y) = 2u(x)u(y) exp = 2u(x)u(y)…

A:

Q: The joint probability density of X and Y is f(x, y). Find the marginal density of Y at 1.4. Round to…

A: The joint probability distribution is given by, f(x,y) = 2xy0&lt;x&lt;1, 0&lt;y&lt;2,…

Q: In order to estimate how much annual income that their graduates earn after graduating, York U…

A: the average income 53450the SD is 5530the sample size is n=186.

Q: If X, Y have some bivariate density, prove that Var(X – Y) = V ar(X)+Var(Y) – 2Cov(X,Y). | (justify…

A: The objective is to show var(x-y)=var(x)+var(y)-2 Cov(x,y)

Q: Let X,Y have joint pdf fX,Y (x,y) = x + y,for 0 < x,y < 1 i) Find the marginal pdfs of X,Y ii) Find…

A:

Q: Let (X,Y) have the joint density function f(x,y) = { (6/5)(1+x+y) for 0 s x, y s 1, x+ys1 otherwise…

A: Given the joint density function of (X,Y) as fx,y=651+x+y     for  0≤x,y≤1 , x+y≤1         0…

Q: Q5) If X and Y have the joint density function f(x, y) = + xy 0< x < + dr).

A: Given,the joint probability function of X and Y as- fx,y=34+xy ; 0&lt;x&lt;1,0&lt;y&lt;10          ;…

Q: Find the marginal densities g(x), h(y), and the conditional density f(ylx). Use f(y|x) to find P(1<Y…

A: Given that, the joint pdf of (x,y) is,

Q: F(x, y) = (1 − e¯¤x)(1 – е¯³µ), for x ≥ 0, y ≥ 0 and a, ß > 0.

A: The joint cdf of X and Y is

Q: Suppose the joint density of X and Y is given by [6xy(2-x-y), 0<x< 1,0 <y<1 otherwise Compute the…

A:

Q: 3. Let (X,Y) have the following joint density function: J ?y? 0<x < 2 , 0< y < 2 f (x, y) otherwise…

A:

Q: Let the joint density function of X and Y be given by c(x + y), for 0 <x < y < 1, f (x, y) = 10,…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: (3) Consider two variables Y₁, Y₂ whose joint probability density func- tion is given by f(y₁, y2) =…

A: (a) To find the marginal density f1(y1) of Y1, we need to integrate the joint probability density…

Q: Suppose that the Second Derivatives Test is applied to a real-valued function z = f(x, y), whose…

A: Given real value function is z=f(x, y) and second derivatives are continuous on the disk D centered…

Q: Smith and Jones are financial analysts who enter a stock picking contest. Smith picks the stock of…

A: Given: Joint density function, fx,y=23x+2yfor 0&lt;x&lt;1 and 0&lt;y&lt;1Probability of…

Q: Suppose we have the following joint density function S6(1 – 42), 0 0, Y2 < 0.2) 2.

A: Marginal density of Y1 is given by, f(Y1)= integration|01 f(Y1,Y2)dy2 = Integration|01 6(1-y2)dy2 =…

Q: x²y- ry f(x, y) is continuous at (1, 1). x- y+1

A:

Q: Consider the following joint density (with support shown in the graph): 3 f(y1, Y2) : 91, 41, 0< y1,…

A: The joint distribution of Y1 and Y2 is   fy1, y2=29y1,    0≤y1,    0≤y2,    y1+y2≤3,0,…

Q: Problem 8: Consider the density function f(x) = a) Evaluate k. b) Find F(x). c) Use F(x) to evaluate…

A: Given: f(x)=kx4,x&gt;10,x≤1

Q: If f (x) = c (9 – x²) for 0 < x < 3 is a density then c is equal to

A:

Q: The joint probability density function p(x, y) is given by: p(x,y) = Axy2      if       0 ≤ x ≤ 6…

A:

Q: Let X and Y have the joint PDF f(x,y) = 2e−x−y for 0<x<y<∞. Find the joint PDF of Z = 2X and W = Y −…

A: f(x,y)°2e−x−y ; 0&lt;x&lt;y&lt; ∞

Q: Lây ởy - Find the bounded solution of- ,x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0.

A:

Q: 2. The random variables X and Y have joint density p(x, y) = = {cry Jcry(1-x) if 0<x< 1, 0<y<1,…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Let X and Y have joint pdf given by f(x, y) = (k(1 − y) if (x, y) ∈ R 0 otherwise, where R is the…

A:

Q: 4. Let X and Y have the joint density f(x, y) = What is P(X>Y > 2) ? e-(x+y) {"th for 0 ≤ z, y<∞…

A:

Q: 51. Calculate P(0 < x < 2; 1 < Y < 2), where X and Y have joint prob- ability density function (2xy…

A: Given information: The two random variable X and Y. The joint probability density function of X and…

Q: Let X and Y have joint CDF Fxy(x,y) = (1/16)xy(x+y) for 0&lt;= x &lt;= 1/2 and 0 &lt;= y &lt;= 2.…

A: In the above answer, the probability 𝑃(1&lt;𝑋≤2,1&lt;𝑌≤2)P(1&lt;X≤2,1&lt;Y≤2) is zero because the…