Let Y be a discrete random variable.  Let c be a constant.   PROVE  Var (Y) = E (Y2) - E (Y)2

Q: Determine if the constant process X(t) = A where A is a random variables with mean? A and oj is mean…

A:

Q: : Discrete random variables X and Y have the joint PMF| c(r+ y)², x= -1,0, 1; y = -2,0, 2,…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: A random variable Y is defined as X3 Y = 2 - X² + 3 Find the density of Y.

A:

Q: Let X be a random variable that follows U (0, 2). Define another random variable Y such that Y = -…

A: We have given that, Let X be a random variable that follows U(0,2).   The probability density…

Q: 3. Let X and Y be two continuous random variables with joint pdf 4.xy, if 0 < x < 1,0 < y < 1 f(x,…

A: Dear Student, As this question has multiple parts, we are allowed to solve only the first…

Q: Suppose that X,Y are jointly continuous random variables with the joint probability density function…

A:

Q: Suppose that two continuous random variables X and Y have joint probability density function fxy =…

A: From the given information, Consider, Consider, EX=∫12xfxdx…

Q: Let X and Y be two continuous random variables with joint probability density 3x function given by:…

A: We know that, Var(X)= E(X^2)-(E(X))^2 so from the given values, = (3/5)-(3/4)^2 = 3/5 -9/16 =…

Q: Let Y1 =;(X2 - X2), Y2 = X2 where X1 and X2 are stochastically independent random variable each…

A:

Q: If X be a continuous random variable with be -bx if x >0 f(x)= otherwise then the moment generating…

A: The random variables can be categorized into 2, continuous random variable and discrete random…

Q: 10. Let Yı, Y2., Yn denote a random sample from the probability density function given by (0+1)y", 0…

A: Given: fy|θ=θ+1yθ,      0&lt;y&lt;1, θ&gt;-10,                 elsewhere The maximum likelihood…

Q: Let X be a random variable with characteristic function p(t). Prove: if I lp(t) – a| dt <∞, then we…

A: Given:The characteristic function φ(t) of a random variable X is defined as φ(t)=eitxAlso,…

Q: Let X be a continuous random variable with domain D = [0, 7] and PDF 0 <x < 2, 2<r < 5, 2a

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

Q: X and Y be two discrete random variables with a joint p en by X-0 X-2 Y=1 0.03 0.02

A: to find P(X&gt;0 and Y≤3)

Q: Let X be an exponential random variable with parameter = 7, and let Y be he random variable defined…

A: Given Let X be an exponential random variable with parameter lamda = 7, and let Y be the random…

Q: 2. Let X and Y be two jointly continuous random variables with joint PDF fxy(x,y) = x + cx² 0≤x≤ 1,0…

A: It is given that X and Y be two jointly continuous random variables with joint pdf fXY(x,y) = x +…

Q: Let the joint pdf of random variables X, Y be fx,y (r, y) = axye-2-3y, for all æ > 0, y 2 0. Find a,…

A: We have given that a joint pdf of variables X and Y.

Q: Let X and Y be continuous random variables with joint distribution function,   F (x,y).  Let g…

A:

Q: Let X and Y be continuous random variables with the following joint pdf: fxy (x, y) = { S Ax +1 +y…

A: Given: The joint density function given is shown below fX,Yx,y=Ax+1      x+y&lt;1, x,y≥00…

Q: 2. Let X be a random variable with pdf fx(x), and Y = X². %3D (a) Find fx(x|X > 0) (b) Find fy(y|X >…

A: We have to answer questions based on conditional pdf of distribution

Q: Suppose that two continuous random variables X and Y have joint probability density function fry =…

A: From the given information, c.

Q: Let X,Y be non-negative simple random variables. If Y SX a.s., then EY S EX.

A: Let X , Y be non negative simple random variables  If Y&lt;=X as then E(Y) &lt;=E(X)

Q: Let X be a random variable with the gamma probability density function. Derive the MSE of T=X2+2X

A: Gamma distribution: It is a continuous random variable, with the probability density function of…

Q: Let X be a random variable with probability mass function  P ( X = 1 ) = 1/2 , P ( X = 2 ) = 1/3 ,…

A: Solution: The given probability mass function of X is

Q: Var (Y) = E (Y2) - E (Y)2

A: Given that y be a continuous randomvariableThen, we know

Q: The joint PDF of two jointly continuous random variables X andY is c(x² + y²) for 0 < x < 1 and 0 <…

A:

Q: 4. The joint PDF of two continuous random variables X and Y is given by fx+y 0<x<1, 0<y < 1 S(x, y)…

A:

Q: If X is continuous random variable then the first moment about the origin is defined to be E(X): -…

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Q: A/ For the r.v. X is given f(x) = ()*; x = 1,2,3,... a- Find the moment generating function. a- Find…

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Q: If f(x) = e-";0 < x < ∞ denotes the pdf of a continuous random variable X, then find P(-1< X < 2) =…

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Q: 4. Suppose that the random variable X has density function 0, fx(x) = x < 0 0 < x. 4e-4", and…

A:

Q: if x be a random variable with moment generating function m,(t) = (0.6 + 0.4e')1º then E(x)= %3D

A: If moment generating function is given then we can find the expected value of the variable by using…

Q: let X and Y have the joint density e-(x+y) for 0<x,y<∞ f(x.y)= other wise then X and Y are…

A: Solution: From the given information, the joint density function of X and Y is

Q: The joint PDF of two jointly continuous random variables X and Y is S(x2 +y?) for 0 < x < 1 and 0 <…

A: We have given that,  X and Y two continuous random variables having PDF is,

Q: Let X1 and X2 be continuous random variables with the joint probability - function fx1,x,(x1, x2),…

A: Hello! As you have posted 2 different questions, we are answering the first question (2.2.5). In…

Q: The joint PDF of two jointly continuous random variables X and Y is Sc(a? + y²) for 0 < x < 1 and 0…

A: From the given information, fx,y=cx2+y2, 0≤x≤1, 0≤y≤1 c=32EY=58 EY|X=32X2+143X2+1 Consider,…

Q: Suppose that the random variables X and Y have the following joint probability density function.…

A:

Q: let X and Y have the joint density e (x+y) for 0<x,y<∞ f(x.y)= other wise then X and Y are Not…

A: Answer: Stochastically Independent.

Q: Let X and Y be jointly continuous random variables with joint PDF 6e-(2x+3y) x, y > 0 fx,x(x, y)…

A:

Q: Let X,Y be two random variables with joint probability density function f(x,y) = ,0< X < Y < 2. Find…

A: Let X, Y be two random variables with joint probability density function fx,y=12 ; 0&lt;X&lt;Y&lt;2…

Q: Suppose (X; Y) is a continuous random vector with joint probability density function fx,ylx.v) = { y…

A: E((x-3)^2)=4.333 (b)

Q: Let X1, X2, ..., Xn denote a random sample from the probability density function fx(x) = ax for x E…

A: Given : fX(x) = αxα-1    for x ∈(0,1) and  α&gt;0.

Q: 1. Let X and Y be two jointly continuous random variables with joint pdf f(x,y) = {k(x + y), 0≤x≤…

A: Given that                      We have to find  Var(X)  And  P(1/2&lt;X&lt;1, 0&lt;Y&lt;1/2)

Q: If the joint pdf of a two dimensional random variable (X,Y) is given by xy ху 0 <x<1&0< y < 2 + f…

A: Given information: Let X and Y be two random variables there joint pdf is given by; f(x,y)=x2+xy3…

Q: Let X1, X2,..., X, denote a random sample from the probability density function fx(x) = axa-l for r…

A:

Q: let x,y be two random variable with joint probability density function -1 0. 0.1 0.2 0.1 1 0.2 0.1…

A: The required expectations E(X| Y=0) means the expected value of X when given that Y is equal to 0.

Q: .Let X be a random variable with the gamma probability density function. Derive the MSE of T=X² +2X

A: Here, X~Gammaθ,n,n&gt;0,θ&gt;0 and T=X2+2X