A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y) is given below. Complete parts (a) through (d) below. f(x,y) = x+y², 0≤x,y≤ 1, f* 0, elsewhere E(XY) = (Simplify your answer.) C (a) Determine whether or not X and Y are independent. X and Y independent, since f(x,y) equal to where g(x) and h(y) are the (b) It is of interest to know something about the proportion of Z=X+Y, the sum of the two proportions. Find E(X+Y). Also find E(XY). E(X+Y)= (Simplify your answer.) of X and Y, respectively.

Q: Let X refer to the sum of two rolled die. Describe the probabilities of each outcome. If pX(x) is…

A: It is given that x denotes the sum of two rolled dies.

Q: Let X be a random variable with the probability distribution below. Find Horx), where g(X)= (2X+3)-.…

A:

Q: Calculate the expected value of X, E(X), for the given probability distribution. E(X)= X P(X = x)…

A: Given probability distribution of X is,x2468P(X = x)We need to calculate the expected value of X.

Q: What is the probability that Randolph stays within the restaurant for at most 18 minutes, i.e.…

A:

Q: 3. A quality engineer at a manufacturing company is keeping track of the number of parts that are…

A: Let X = the number of parts out of the tolerance bounds from first shift and Y = the number of parts…

Q: Let the joint probability function for Y, and Y2 be Y1 Y2 0 0 3/202/200/20 3 6/20 0 9/20 3 E[ ECY I…

A:

Q: rts (a) through (d) belo 2+2 1².1 0sx elsev X), Var(Y), and Cov(X) r answers.) 7 r answer.)

A: The joint probability density function for (x,y) is given below f(x,y)=94x2+34y2    0≤x,y≤10…

Q: Consider the joint probability distribution below. Complete parts (a) through (c). Y Y 0 1 0 1 Pw…

A: Given that: Joint probability distribution:     X     1 2 Y 0 0.30 0.10   1 0.40 0.20

Q: You have two fair coins. The first coin is tossed five times. Let the random variable X be the…

A: Let X be the number of heads when we toss the coin five times. Then X represent a Binomial…

Q: Example . Let the random variable X of the continuous type have the p.d.f. Ax) = 2/x', 1 <x < o,…

A:

Q: Let the r.v. X assume the value 'r' with the probability law : P(X = r) = q-¹ p ; r = 1, 2, 3. Find…

A: The probability mass function of X is given as-

Q: Consider the two random variable X and Y. They have the following joint probability mass function: 1…

A: The correlation of X and Y is represented by the coefficient of correlation. For two random…

Q: The common probability function of X and Y random variables like this a. Find the value of Cov (X,…

A:

Q: Let X and Y be dependent random variables. Which statements are always true? Select one or more:…

A: # Let X and Y be dependent random variables. Which statements are always true?

Q: Let X be a random variable with the probability distribution below. Find Hg(x) where g(x) = (2x +…

A:

Q: Property 4. If X is a random variable and a and b are constants, then E (a X + b) = a E (X) + b,…

A:

Q: In a M/M/1 model, the average number of customers in the system is 14. Then, the probability that…

A: We have given that  Number of customers in the systems is (Ls)=14

Q: Two fair dice are rolled. Find (In tabular form) the joint and marginal probability mass functions…

A: Here given that two fair dice are rolled. Find the joint and marginal distribution of X and Y where…

Q: Let X and Y be discrete random variables with joint probability function: P( x, y ) = ( 2x + y )/12,…

A: Let X and Y be discrete random variables with joint probability function:P( x, y ) = ( 2x + y )/12,…

Q: Find the probability distribution for Y. The table for the probability distribution of Y may have…

A: Here, Y = X^2 + 1

Q: Consider the joint probability function: X 1 2 -1 а 0.1 d. c 0.3 0.4 1 If X and Y are independent…

A: Given:

Q: The distribution of random variable X can be described by the following probability mass function:…

A: The probability mass function for the X can be defined as:

Q: The random variables X1,..., Xn are independent and identically distributed with probability…

A: Given information: The probability density function of the random variables X and Y is given.

Q: he table below shows a probability density function for a discrete random variable X, the number of…

A: Ans#- The table below shows a probability density function x P(x) 0 3/20 1 1/20 2 1/4 3…

Q: X is a continuous random variable with the probability distribution (density) graphed above. The…

A: To find the probability that X is between 0.2 and 0.4 we have to find the area of the shaded region:

Q: In a M/M/1 model, the probability that the system contains exactly one customer is 0.218. Then, the…

A: Given: The queuing model is M/M1. Let X be a random variable representing the number of customers.…

Q: f(x, y) = x² + y² 62 (a) Find P(X= 2, Y = 1). Ans. where x = 0, 1, 2 and y = 0, 1, 2, 3 and f(x,y) =…

A: It is given that the joint probability function of two random variables X and Y.     Note: According…

Q: Please show work. X and Y are two discrete random variables having the joint probability…

A: Cov(X,Y)=E(XY)-E(X)E(Y)corr(X,Y)=Cov(X,Y)V(X)V(Y)

Q: Contracts for two construction jobs are randomly assigned to one of or more of three firms, A, B,…

A:

Q: The diagram shows the probability density function of a continuous Random Variable X. What is the…

A: Here the given graph is      we have to find the value of b

Q: The distribution of the random variable X is described by the following probability distribution…

A:

Q: Value x of X P(x =x) -6 -5 -4 0.12 -3 0.17 3. 0.15

A:

Q: Decide whether the random variable X is discrete or continuous. X represents the tension at which a…

A: Introduction A variable is any characteristic that is being measured.

Q: Find the value of k. Determine and justify if L and W are independent. Find the conditional…

A: here as per guidelines i have calculated 3 subparts plz repost for remaining here given joint…

Q: fx(x) 4 a -1a

A: We have to find the value of constant for valid pdf.

Q: Let X be a random variable with the probability distribution below. Find g(x), where g(x) = (2x +…

A: Given datax          -3        6         9f(x)       512      112      12andg(x)=(2x+3)2

Q: Answer d, c, f

A: We want to calculate the mean and conditional mean

Q: Find E(x) and Var(x) of X, where X is the discrete random variable whose probability table is given…

A:

Q: Find the marginal probabilities of each random variable X and Y in the following table: - Compute…

A: