[Q1] The joint density function of the continuous random variables X and Y is expressed below. Find: (a) the value of the constant c, (b) P(X > 2, Y < 1). ce³-2-4y, for 1

Q: Let the joint density of the continuous random variables X ({ (1² + 2 xy) if 0 < x < 1; 0 <y<1 f(x,…

A: This is a problem of joint distribution.

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A: According to the Bartleby guidelines experts solve only one question and rest can be reposted

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Q: 3. The continuous random variables X and Y have known joint probability density function f (x,y)…

A: Let the random variable Z = max(X, Y).

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Q: Let (X,Y)be a continuous random variables with joint pdf given by y Osxs2,0sys1 lo otherwise fx,…

A: The provided information are:

Q: i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).

A: The joint probability distribution function of X1 and X2 is given and first we have to determine the…

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A: Given: fy1, y2=6y12y2,       0≤y1≤y2, y1+y2≤20,               Otherwise Required P(Y2 &lt; 1.1 | Y1…

Q: Let X and Y be jointly cantinuous random variables with joint PDF is given: $ X,Y (x.y) = (1+x*y)…

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Q: a) Find marginal density functions. Are Y1 and Y, independent? b) Find P(0 < Y < 0.3, –2 < Y2 < 1).…

A: given  f(y1,y2) = 6(y12 + y1 . y2/2) /7  ,   0&lt;y1&lt;1  ,0&lt;y2&lt;2

Q: Choose two numbers X and Y independently at random from the unit interval [0, 1] with the uniform…

A: X and Y are Independent uniformly distributed random variables on the interval [0,1]. The joint PDF…

Q: i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).

A: The joint PDF is given and first we have to determine the marginal pdf of X2 to find the required…

Q: Let X and Y be random variables with joint density f(x, y) = (x - y) if x = [0, 1], y € [-1, 0]…

A: The conditional probability is defined as :   P(X|Y) = P(X,Y=y)P(Y=y)

Q: Let X ∼ Uniform (0, 2). Consider a square with sidelength X. (a) Express the area A as function of…

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

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A: It is an important part of statistics . It is widely used .

Q: 2. Let f (x, y) be the probability density function of the continuous random variable (X,Y). If U =…

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Q: Let X₁ |Z| where Z N (0, 1) and X₂ variables. Let Y₁ = X² + X², Y₂ = X₁. Find the joint density of…

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Q: Let continous random variable x taking on values over the set [0,a] and has a probability density…

A: It is required to find the value of the constant C.

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Q: 2. The continuous random variables X and Y have known joint probability density function 4x 0≤ y…

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Q: a) Find the value of the constant k. b) P (X> 1⁄2) =?

A: Note*: As per guidelines, we can answer only one question at a time. I request you to please repost…

Q: Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1],…

A: Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1],…

Q: Let X ∼ Unif(0, 1). Let g(x) = e x and Y = g(X). (i) Find the density fX of the random variable X.…

A: Given  X~ U(0,1) We want to find the pdf of x, Cdf of Y and pdf of Y

Q: Show E(Y)

A: First we have to determine the marginal pdf of Y to calculate the value of E(Y).