Let X be a random variable with mean ux=20 and standard deviation x = 3 and...

Let X be a random variable with mean ux=20 and standard deviation x = 3 and let Y be a random variable with mean uy=28 and standard deviation y =3. It is known that X and Y are independent random variable. A new random variable U is created where U=Y-X. what is the standard deviation of U?

Solutions

Expert Solution

X and Y are independent random variable

standard deviation of X = 3

Var(X) = variance of X = 9

standard deviation of Y = 3

Var(Y) = variance of Y = 9

U = Y-X

Var(U) = Var(Y-X)

Var(U) = Var(Y) +Var(X) - 2Cov(X,Y)

[ Cov(X,Y) is covariance of X and Y

Here Cov(X,Y)=0 as X and Y are indepenent]

So, Var(U) = Var(Y) +Var(X)

Var(U) = 9 + 9 = 18

standard deviation of U = = 4.2426

Answer : Standard deviation of U is or 4.2426

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose that X is a random variable with mean 20 and standard deviation 5 . Also...

Suppose that X is a random variable with mean 20 and standard deviation 5 . Also suppose that Y is a random variable with mean 45 and standard deviation 12 . Find the variance and standard deviation of the random variable Z for each of the following cases (Give your answer to three decimal places.) a) Z = 4 + 11X b) Z = 11X − 4 c) Z = X + Y d) Z = X − Y e)...

Let X be a random variable with mean μ and standard deviation σ. Consider a new...

Let X be a random variable with mean μ and standard deviation σ. Consider a new random variable Z, obtained by subtracting the constant μ from X and dividing the result by the constant σ: Z = (X –μ)/σ. The variable Z is called a standardised random variable. Use the laws of expected value and variance to show the following: a E(Z) = 0 b V (Z) = 1

Let x be a normal random variable with mean 35 and standard deviation 2. a. Find...

Let x be a normal random variable with mean 35 and standard deviation 2. a. Find P(30 < x < 38). .9270 b. Find P(x > 34). .6915 c. Find P(x = 36). 0 d. Find the area under the distribution of x to the left of 31. .0228

1) Let X be a normally distributed random variable with a standard deviation equal 3

1) Let X be a normally distributed random variable with a standard deviation equal 3; i.e. X∼N(μ, σ=3. Someone claims that μ=13. A random sample of 16 observations generate a sample mean of 14.56. a) Does the sample mean provide evidence against the above claim at 5% significance level? Complete the four steps of the test of hypothesis: b) Assume that X was not normal; for example, X∼Unifμ-3, μ+3 which would have the same standard deviation. Use simulation to...

Part A: Suppose a random variable X have mean of µ and standard deviation σ. Let...

Part A: Suppose a random variable X have mean of µ and standard deviation σ. Let a and b be constants. i) Derive the expected value of aX + b. ii) Derive standard deviation of aX + b Part B: Suppose that in country A, the price of certain good has a mean of $100 and a variance of 25, in A-dollars. Country B has a fixed exchange rate with A so that it takes 2 B-dollars to buy 1...

Given a random variable X following normal distribution with mean of -3 and standard deviation of...

Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal. (1)Find the distribution of Y, i.e. μy,σy (2)Find the probabilities P(−4<X<0),P(−1<Y<0) (3)Find the probabilities P(−4<X¯<0),P(3<Y¯<4) (4)Find the 53th percentile of the distribution of X

Suppose x is a random variable with a mean of 40 and a standard deviation of...

Suppose x is a random variable with a mean of 40 and a standard deviation of 6.5 that is not necessarily normally distributed. (a) If random samples of size n=20 are selected, can you say the sampling distribution of the means, the (x bar) distribution, is normally distributed? why or why not? (b) if random samples of size n=64 are selected, what can you say about the sampling distribution of the means, (x bar)? is it normally distributed? what is...

Given a random variable ? has population mean ? = 20 and standard deviation ? =...

Given a random variable ? has population mean ? = 20 and standard deviation ? = 5. a.) For the sampling distribution of the sample mean ?, for ? = 50 trials what are the mean and standard deviation? ??bar = _____________, ??bar =_____________. b.) What is the probability that the sample mean will be in the interval 19 < ?bar < 21 ? ?(19 < ? < 21) =_____________. (give answer to at least 4 signifiant figures.)

Given that x is a Normal random variable with a mean of 10 and standard deviation...

Given that x is a Normal random variable with a mean of 10 and standard deviation of 4, find the following probabilities: (6 points) P(x<6.7) P(x>12.5) P(8.8<x<12.5)

If x is a binomial random variable, compute the mean, the standard deviation, and the variance...

If x is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases: (a) n=3,p=0.9 μ= σ^2= σ= (b) n=6,p=0.1 μ= σ^2= σ= (c) n=4,p=0.6 μ= σ^2= σ= (d) n=5,p=0.8 μ= σ^2= σ=

Subjects