In a car service station, there are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function for (X, Y) is given by f(x,y) = {6." S{(² + y³), 0sx s1;0sy s1 elsewhere. (a) If Z= X+ Y, the sum of the two proportions, find E(Z) ; (b) Find E(XY ); (c) Find Var(X); (d) Find Cov(X, Y );

Q: SV) ="(3y² Sh(3y² + 2) ; -2<ys2 0; otherwise

A:

Q: Suppose that X and Y have the following joint probability function: 3r, if0<y< a<1 0, f(x, y) =…

A:

Q: We have three independent risks, each having the following probability mass functions: P(X₁=0)=1/4…

A: To calculate the VaR(90%) and TVaR(90%) of the distribution of the total claims of the portfolio of…

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: Given that 40% of fruit flies of fruit flies posses a certain gene. So, probability that a fruit fly…

Q: For the given probability distribution, X f(x,y) 1 2 5 0.25 0.2 y 10 0.2 0.15 15 0.15 0.05 Determine…

A:

Q: Let X,Y be two random variables with joint probability density function Y Values 23 O 18 000 1/8 1/8…

A: Probability could be defined as a number that always falls between 0 and 1, where 0 implies the…

Q: . Given that (x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution…

A: Answer - Given that    joint probability distribution function of x and y                       f(x,…

Q: function f(x)=B³ Find the Maximum Likelihood Estimator of B. 00 elsewhere

A: Solution

Q: 6) The joint probability density function of two random variables, X and Y is given by [2 - 2pry +…

A:

Q: 3. Find the probability mass function of the random variable Y which represents the number of red…

A: Introduction: The random variable Y is the number of red marbles when 3 marbles are drawn at random…

Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Find the distribution functions and con- ditional cdf's.

A:

Q: Question 4. The random variables X and Y have the joint pdf given by fxy(r, y) = e*, I> 0, 0 < y <…

A: We have given that  The random variables X and Y have the joint pdf given by fXY(x, y) = e-x.…

Q: Suppose that a > 0 is a constant. Let the joint pdf of random variables X, Y be fx,Y (x, y) x > 0, y…

A: To determine the value of the constant a, use the fact that ∫-∞∞∫-∞∞fx,ydydx=1. The conditional…

Q: 5. and Y is The joint probability distribution function of two discrete random variable |x -y| 15…

A:

Q: ion of (X, Y) is larger than the area below the distri at, random variable 5) of (X, Y), for any…

A:

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: 1. Explain how to generate a random variable X distributed as the Cauchy distribution, whose…

A:

Q: 5. Suppose that X is a discrete random variable with probability density function х%3D1, 2, 3, 4.…

A: In question, We have given the pdf of X which is f(x). Then we'll find the value of E(X). The…

Q: 7. The probability mass function (PMF) is expressed as PMF = P(X = k) = - k(k +1) म्कग ,k =1,2,..,0…

A:

Q: For a given electronic component, it has been shown that it is necessary to restart once every 250…

A: INTRODUCTION:  Definition: Conditional Probability  suppose A and B are any two events. the…

Q: what is E[XY]?

A:

Q: Suppose X₁,..., Xn are independent exp(X) random variables, where is the rate parameter. Find UMVUE…

A: Let X1, ......Xn are the independent exp(λ) random variables,where λ is the rate parameter.X¯ is a…

Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

A: Solution: The covariance between the random variable X and Y can be defined as  Cov(X,Y)= E(XY)-…

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: ✅✅✅✅✅✅✅

A: To test the claim that there is no difference in heights between mothers and their first daughters,…

Q: B) Let X and Y be discrete random variables with joint probability function 2-y+1 9 for x = 1,2 and…

A:

Q: the joint density: fX,Y(x,y) = 2−x−y,    for 0<x<1, 0<y<1                   0,…

A: Dear students as per guidelines we answer the first three subparts only.

Q: I have true false questions.(There is no need to explain, it is enough just to write true or false.)…

A: 1) False   Because E(Z1*Z2) ≠ E(Z1)*E(Z2)

Q: Consider the formula: P(x) = x2/21, x = 0, 1, 2, 4. Is P(x) a probability mass function? If so, show…

A: Solution: 9. From the given information,

Q: If X and Y are both random variables with a joint probability distribution: Se-(z + y), r > 0, y >…

A:

Q: 2) Consider the random variable Y has a normal distribution with the following probability density…

A: Given Y follow normal distribution and its probability density function is shown below…

Q: If X is a continuous random variable with p. d.f. (X f(x) = }6 ,0 <x< 3 12 ,othewise

A: Given pdff(x)=x6+112,0≤x≤30otherwise The probability distribution of Y is calculated as shown below.…

Q: 5. Suppose that X is a discrete random variable with probability density function x = 1, 2, 3, 4.…

A: Given: p(x)=cx2

Q: Determine the value for c and the covariance and correlation for the joint probability mass function…

A:

Q: Find the marginal pdf's

A: