Answered: Let X and Y be independent random…

Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. How can we prove that 2X and 3Y are independent? What is the standard deviation of 2X + 3Y?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: The random variables are x and y. The mean and standard deviation is: x is 12 and 5 y is 10 and 2 Of…

A: Given, X and Y are two random variables ,Where ,Mean of X , E(X) = 12 Standard deviation of X ,…

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3 We know…

Q: Suppose that X is a random variable which only takes on non-negative values, with mean 5 and…

Q: Let X₁, … … …‚ X„ be an independent trials process with common expected value 3 and common variance…

A: a) 1) The independent process is X1 ....Xn , Let S = X1 + X2 +.....Xn , Expected value of S is…

Q: If X is a continuous random variable with mean μ and standard deviation σ, what is the probability…

A: Answer: Approximately 68% of the values of X are expected to lie between μ - σ and μ + σ. This is…

Q: et χ2 = Z12 + Z22 + … Zdf2 is chi-square distribution random variable, where df = 4. What is the…

A: Given that X2=Z12 +Z22+.....+Zdf2 is chi-square distribution random variable Where, df=4

Q: Show that adding a constant K to a random variable increases the average by K but does not change…

A: Suppose I have a below data For random variable X 2,5,8,4 consider k= 2 Average of 2,5,8,4 using…

Q: Show that, if the random variable X has an F-distribution with ν1 and ν2 degrees of freedom, then Y…

A: If there exist two independent variables with degrees of freedom v1,v2 is the random variable of…

Q: Find P(A), given that P(A) 0.493.

A: Given, P A=0.493

Q: Let ZZ be a discrete random variable taking one of the four distributions covered in Chapter 10.…

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: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 24 psi.…

Q: 2Y 0 Show that has a x² distribution with 2 degrees of freedom.

A: Mean =θ ,

Q: X is a positive discrete uniform random variable. The mean and the variance of X are equal to…

A: Given,X is a positive discrete uniform random variable with mean = 6 and variance = 4.We need to…

Q: Suppose that a poll of 18 voters is taken in a large city. The random variable x denotes the number…

A: Solution-: Given: n=18,p=0.43 (Or 43%) What is the mean and standard deviation of X?

Q: Suppose that X is a continuous random variable that follows a normal dis- tribution with mean 68. If…

A: Solution: Let X be the continuous random variable having normal distribution with mean μ= 68…

Q: Let X ∼ Binomial(n, p) with n known. Find the maximum likelihood estimator of p. What is the (exact)…

Q: What is the distribution of X? 1) Out of the 38 pizzas that you try, how many would you expect to…

A: Let p be the probability of you liking the pizza. Given that p = 0.08

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Suppose data X1, ..., Xn are sampled from the population, sample mean is a random variable

A: It is given that Sample : x1, x2,......,xn

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 that X is a continuous random variable with a Gamma distribution, that the Expected Value of…

A: It is given that X is a continuous random variable with a gamma distribution, with Expected value…

Q: Let ξ and η be independent standard normal random variables. Find the distribution of X = ξ/η

Q: Suppose Y is a normally distributed random variable and Y=In(5X²). It is known that the mean and…

A: Given that is a normally distributed random variable, and .The mean and standard deviation of are…

Question

Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. How can we prove that 2X and 3Y are independent? What is the standard deviation of 2X + 3Y?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introducing the given information

VIEW

Step 2: Calculating standard deviation of 2X + 3Y

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let X1 , X2 , X3 be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The mean and variance of p-hat = 1/n ( X1 + X2 +... Xn ) . E(p-hat)= p Var(p-hat) = p(1-p) / n
Let X1, X2, X3, .., X36 be independent skewed random variables with mean ux = 3 and standard 2. Let X be the distribution of the mean of these 36 random variables, namely deviation ox X = X1+X2++X36 36 (a) What is the approximate shape of the distribution of X? (b) What is the mean of the distribution of X? (c) What is the standard deviation of the distribution of X? (d) Can we determine P(X < 2.5) using a z-score? You do not need to compute this probability, just answer yes or and briefly explain why or why not.
the maximum likelihood estimator of a random variable x with uniform distribution U(0, 0), 0 = max(x₁.x). Is the estimator biased?
Find the standard deviation of a discrete random variable X which satisfies P(X=1)=0.1,P(X=-1)=0.6, P(X=2)=0.3.
Consider two independent random variables X and Y with Means of 17 and 21. Assume the variance for the first variable is 1 and that for second variable is 2. Define a new variable as: 3 *X + 4*Y 3*X- 4*Y Calculate the new mean and variance for each case.
Let X be the Random Variable: x 0 1 2 = x) P(X= 0.5 0.2 0.3 Let X1, X2 be the identically distributed Random Variables so that X1, X2 ~ X. Find the expected value and variance of both X and X1 + X2.
Let X be a random variable with a uniform distribution over the interval [-2 , 4]. Determine the standard deviation of X.
X is a random variable with mean 30 and standard deviation 4. Y is a random variable with mean 50 and standard deviation 8. Find the mean of random variable Z for each of the following cases. Please show your work. 1) Z=12X-5 2) Z= X-Y 3) Z= -2X+2Y
Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a] How can we prove that 2X and 3Y are independent? [b] What is the standard deviation of 2X + 3Y?
Assume that X₁, X2,..., Xn are independent and identically distributed random variables with expectation and finite variance o2. What is the approximate distribution of Sn = X₁ + X₂ + + Xn? (State all parameters of the distribution.)
Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).
Z and T are random variables that are normally distributed. The Mean of Z is 5 and its standard deviation is 3. The Mean of T is -2 and its standard deviation is 6. what's r and e, both greater than 0 so that P(4 < T < 16) =P(r< Z < e)