Given that X and Y are independent random variables and E(X) = 4, E(Y) - 7, Var(X) = 3. Var(Y) = 6. find Var(10X - 3Y).

Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

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: (TRUE / FALSE) For two random variables, X and Y, Var(X+Y) = Var(X)+Var(Y) if X and Y are…

A: Let X is a random variable. Then the variance of X, denoted by Var(X), is a measure of dispersion of…

Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

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

A: 40% of the fruit flies posses certain gene. So, probability that a fruit fly posses that gene = 0.4…

Q: A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x-x²+4) =

A: Given that E(X) = 1.5, and var(X) = 0.25 The var(X) is defined as Var(X) = E(X2) - (E(X))2

Q: If X, Y are standardized random variables and r(aX+bY,bX+aY)= 1+2ab a²+b² I Find r(X,Y), coefficient…

A:

Q: X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X +…

A: We want to find V(aX+bY)= ?

Q: If X and Y are independent random variable find covariance between X+Y and X-Y. Answer:

A: Given that X and Y are independent random variables. We need to find covariance between X+Y and X-Y

Q: b) Find the variance Var(X) of X.

A:

Q: Suppose that the random change in value of a financial asset is X over the first day and Y over the…

A: The variance of X+Y is calculated asVarX+Y=VarX+VarY-2CovX,Y

Q: Let X and Y be random variables with variances Var(X) = 1 and Var(Y ) = 2. (Note that X and Y might…

A: It is given that   Var(X) = 1 Var(Y) = 2

Q: Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the…

A: The correlation coefficient between two random variables X and Y is defined as:  ρ(X, Y) = Cov(X, Y)…

Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

Q: show all solution 1. Suppose X is a random variable with E(X2)=10 and E(X)=2. Find the following:…

A: Variance of constant is 0.

Q: Let X be a random variable from a Chi-Square Distribution with 13 degrees of freedom. Tatiana is…

A: We have to answer questions based on chi square distribution.

Q: The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown in…

A: Let X denote the prelim exam Let Y denote the midterm exam Calculation:

Q: Within the interval (0,1)we randomly choose two numbers: x and y . Determine the probability that…

A: The problem can be solved using the concept of basic probability.

Q: find the probability that the number of the red candy is between(E(X)-1) and (E(X)+1)

A: Consider the probability distribution table, X 0 1 2 3 4 5 f 21 29 27 26 18 30 P(X) 21151…

Q: Please explain your answer with steps Suppose X and Y are random variables such that E[X] = -3 and…

A: Suppose X and Y are random variables. Given: E(X) = -3 E(Y) = 6 We have to find E(X-Y). E(X-Y) =…

Q: If 25% of the oranges produced by a farm is defective in a random sample of 20 oranges, then if the…

A: Given 25% of total 20 oranges are defective, To calculate (X>3) if X represents the number of…

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

A:

Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

A:

Q: (a) Find the number of these patients that had either high blood pressure or high cholesterol…

A: A survey was conducted among 68 patients admitted to a hospital cardiac unit during a two-week…

Q: Find the variance of X + 3Y + Z + 6 in terms of the variances and covariances of X, Y, and Z.

A: Given:  X + 3Y + Z + 6

Q: If X Gamma(4,6) the the variance of X is 4 24 144

A:

Q: Find variance of Y1

A:

Q: Let X1 and X2be independent exponential random variables: fX1(x1) = e−x1 and fX2(x2) = e−x2 1

A: # Given:  X1 and X2 be independent exponential random variables: fX1(x1) = e−^x1 and fX2(x2) = e−^x2…

Q: Assume that W(t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) =…

A: This question seeks to determine the probability that the random variable S(12) is greater than 3…