Suppose that X and Y have the joint probability mass function x+y 21 P (X = x, Y = y) = " X = 1, 2, 3 and y = 1,2 (and equals 0 otherwise).

Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: The lifetimes X and Y (in years) of two machine components have joint probability density (5 – x –…

A:

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: 6. If p(r1,12) (2/3)+**(1/3)2--,(1,12) (0,0), (0, 1), (1,0). (1, 1), zero elsewhere, is the joint…

A:

Q: Suppose that we have 2 random variables X and Y with joint probability density function fxy(x,y) = k…

A:

Q: 7) Suppose that the lifetime of an organism has probability density function f(x) = 4xe-2*, with x…

A: Since x=the number of years, so the least value of x is 0.   21) The probability that the organism…

Q: If X and Y are random variables and X is a geometric random variable where p = 0.1 then what is

A: Given information: X is a geometric random variable with p=0.1. Y=sinπX Y=

Q: Suppose X and Y are independent, Cauchy random variables with PDFS specified by fx(x) 1/n and fy(y)…

A: From the given information, f(X)=1π(1+x2)f(y)=1π(1+y2) X and Y are independent. Consider, the joint…

Q: Suppose we have the quadratic function f(x)=A(x^2)+2X+C where the random variables A and C have…

A: Let the quadratic equation is f(x)=Ax2+2X+C. From the question, f(A)=A2     0≤A≤2 f(C)=3C2    0≤C≤1…

Q: Suppose X has the probability mass function p (1) = 3, p (2) = ;, and p(3) = . Then E (2*) is equal…

A: Given,P(1)=13P(2)=12P(3)=16

Q: Suppose that X us a random variable with density function J급(1+z2) if 0 <z<2 0 otherwise f(x) = What…

A: We have given that the random variable X has density function, f(x) = { 3(1+x2)/14,   0&lt;=x&lt;=2…

Q: nd the probability density of the sum W = X + Y.

A:

Q: Is f(r) a legitimate probability mass function? E(1- p)*-'p =p+ (1 – p)p+ (1 – p)°p+ • … 2 1 r=1

A: To be a legitimate probability mass function we must have all the probability between 0 and 1.And…

Q: A random variable W has range RW = {1, 2, 3, . . . } and the probability mass function given by…

A: P(W=k)=1k2kln(2);k=1,2,3...,Objective:Find the expected value of W:Concept Used : Geometric series:…

Q: Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . .…

A: Probability Mass Function :- If X is a One-dimensional discrete random variable taking at most a…

Q: Let R have probability mass function (pmf) p(r)=1/8 for r=1,2,...,8. Fin (1)the cumulative…

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

Q: Let fx,y (x, y) be the joint probability function for the random vector (X,Y) (discrete or…

A: fx(1) = 0 f(1,y) = 0

Q: 48. If two random variables x1 and x2 have the joint probability density f (x1, x2) = - (x + 2x2) }…

A:

Q: 1. The random variable Y = X² does not have a normal distribution because the 1 2 e 1 probability…

A: Given that,  X~ N(u, σ2) Where u is mean and σ2 is variance. P.d.f of X,  f(x)=…

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

A:

Q: (b) Assume that Y₁, Y₂, ..., Yn are independent normal random variables with mean μ = B₁ + B₁x₂ and…

A:

Q: 9 Let the probability density of the two-dimensional random variable (5, n) be (4e", x>0; f(x)=10.…

A: The probability density function for the two variables are : fξ(x)=4e-4x ,x&gt;0fη(y)=6e-6y ,y&gt;0…

Q: A discrete random variable has probability mass function p ( x ) = c x 2 , x = 1 , 2 , 3 . Find the…

A: Probability mass function :  A function f can only be a probability mass function if it satisfies…

Q: a) Calcuate the exact expectation and the variance of X.

A: Given: X = max(10,Y) with Y ~ Poisson λ=13

Q: Experiment X is consist of drawing two balls from a basket containing 13 blue and 5 red balls.…

A: Solution: From the given information, a basket contains 13 blue and 5 red balls. Total number of…

Q: It is known that X = 1,2,3 and 4 = 1,2,3 are two variables with the probability Mass function…

A: We have to find  a...P(X=x/Y=1)  b...P(Y=y/X=1)  c...X and Y are not independent

Q: Suppose X is a random variable with the cdf Fx(x) = 1-(1 + x²) x>0, C70, X>0 Derive the pdf of the…

A: Suppose X be the random variable with the cdf  FXx=1-1+xc-γ  ; x&gt;0, c&gt;0, γ&gt;0

Q: Let A and B two random events and P(A)-1/2, P(B)-1/5. and P(A | B)- 1/4. Assume X-B(1, P(A)) and…

A: Let A and B be two random events and:    Assume:Where B(1, p) denotes a Bernoulli distribution with…

Q: 3. Find the value of k for the probability mass function f(x) = k () ) for x = 0,1,2. %3D

A: We are given a probability mass function and we need to find k and cumulative probability…

Q: 7. Let X be a continuous random variable with probability density function given by Se-(z-z0) x > x0…

A: Let X be the continuous random variable with probability density function is,  f(x) = { e^-(x-x0)…

Q: Suppose that you are looking the N-binomial model with the no-arbitrage assumption with 2 = u = 1/d,…

A: For the N-binomial model described, where the no-arbitrage assumption is given by , and , and the…

Q: 5. Suppose that X is a discrete random variable with probability density function p(x) = cx³, (a)…

A: Given, P (x) = cx2        ,   x = 1, 2, 3, 4         = 0          .  Otherwise     To find, a) Find…

Q: Sahad prides himself in making a burger in under 4 minutes. The time, Y, in minutes to make the…

A: Given pdff(y)=112(y+2)      0≤y&lt;3112(y-2)       3≤y≤4mean=E(y)=∫yf(y)dy

Q: Suppose (X,Y) is a continuous random variables with joint probability d 4xy Osxs1,0sys1 x,Mx.v) = {"…

A: Let X be a random continuous variable with probability density function(pdf) f(x) then the expected…

Q: 7. Let X, and X₂ have the joint probability mass function (pmf) p(x₁, x₂) = X-X₂/36, x₁ = 1, 2, 3…

A: The following solution is provided below:

Q: Suppose X and Y are continuous random variables with joint probability density function (pdf) fxx…

A: f(x,y)=329(xy)1/3;0≤x≤y≤1

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: The joint probability mass function of X and Y is given by (x₁²y₁ P(X = x₁, Y = y) = Pxy(x) = 30 0 x…

A: Joint probability mass function of X and Y is given as: PX=xi,Y=yi=xi2 yi30,    xi=1,2 ; yi=1,2,3