5. Let X, Y be iid random variables each with density fx(x) = for x > 1 and zero otherwise. (a) (b) Find the density of Z = Y/X. Find E[√Z].

Q: Show E(X)

A: Here given joint distribution of x and y

Q: Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table.…

A: The joint probability distribution of X and Y is f(x,y)   1       2       31           1/4    1/4…

Q: A Gaussian random variable X is N 0, 1]. A second random variable Y is independent of X and…

A: From the given information, The random variable X is normally distributed N0,1 Y follows uniformly…

Q: Use the method of moment to estimate the parameter 0 for the density f(;0) =¿I0,01(x) based on a…

A:

Q: 9. If X, Y have some bivariate density, prove that Var(X – Y) = Var(X)+Var(Y) – 2Cov(X,Y).

A: We have given that X and Y are random variables having some bivariate density.

Q: for r, y > 0, f(x, y) = (1+x)2.(1+xy)² > 0, otherwise. Show that X and X Y are independent,…

A: *answer:

Q: wabie values range from x =- oo to o. Find: (i) The CDF F (x) (ii) The relationship between a & b…

A:

Q: Suppose that the random variable X has density fx (x) = 4x³ for 0 X).

A: Independence of pdf applied.

Q: defined by Y=(X-a)2. Find Fy (y) in terms of Fx (x). Hence suppose X is a random Gaussian variable…

A:

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…

Q: fw=X+y, Find the probability density fu of the random vairiable W. g) W= 9, Find. the, probability…

A: where, ∫-∞∞∫-∞∞ f ( x,y ) dx dy = 1 x range is from y to 1,44 and y range is from 0 to x therefore,…

Q: If X is a uniformly distributed random variable in 2 find the density of 2 Y = tan X.

A: Answer: For the given data,

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

A:

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: 3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ +…

A:

Q: Find the density of X = max(Y1,Y2), where Y1 and Y2 are independent random variables with densities…

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

Q: Suppose that the random variable X has density ƒx (x) = 4x³ for 0 4X).

A:

Q: Let X1, X2, ..., X, be independent random variables with the random variable X; having density…

A:

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

A:

Q: If the joint density of X and Y is given byf(x, y) =⎧⎨⎩e−(x+y) for x &gt; 0, y &gt; 00 elsewhere and…

A:

Q: (c) Find the marginal distribution of X and Y. (d) What is Cov(X,Y)? (e) Find the probability…

A: Here we have given the joint probability density function of random variables x and y. We have to…

Q: 6) The random variables X and Y have joint density f( x, y) = x2.y2 for 1sx, 1sy and f( x, y) = 0…

A: The given function is: fx,y=1x2y2           x≥1 , y≥1   Given data: u=xy    and v=x·y   Thus,…

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: (3) Find the density of Y = X² when X ~ Binomial(4, ). The following answers are proposed: (a) P(Y =…

A:

Q: e joint density of X and Y is given by, fxr (x, y) = (x² + 0 1) b) Find the marginal probability…

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

Q: Show E(Y)

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

Q: Consider the random variable X with PDF f(x) = e−x / (1 + e−x)2 , x ∈ R.

A: From the given information,the random variable X has pdf is,

Q: Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass…

A: f(x,y)=c(x+y)   ; x=1,2,3 and y=1,2,3

Q: Show E(XY)

A:

Q: Find E[XY) if fxx) = 2/3 and the joint PDF of the random variables X and Y is zero outside and…

A:

Q: What is the joint probability density function f₁,2 of Y₁ = X₁/X₂ and Y₂ = X₂?

A: We will use Jacobian method of transformation to find the joint probability of Y1 and Y2.

Q: The number of minutes that train is early or late can be modeled by a random variable whose density…

A: Given the density function for the random variable, the number of minutes that train is early or…

Q: Let X be a continuous random variable with density function be-bx for a > 0 otherwise , f(x) = where…

A: Introduction: Exponential Distribution:  The exponential distribution is also called a waiting…

Q: Let X and Y be jointly continuous random variables with joint PDF is given: f X,Y (x.y) (1+x²y)…

A: