Answered: 5.6.1 X and Y are independent, normal…

5.6.1 X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following: a. E(3X+2Y) c. P(3X + 2Y < 18) b. V(3X+2Y) d. P(3X + 2Y < 28)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Q 8.3. Suppose Z₁, Z2 and Z3 are independent standard (univariate) normal random variables. Which of…

A: It is given that are independent standard normal variates.We have to obtain whether the given…

Q: 2. Let X and Y be independent random variables with means ux, Hy and variances o, ož. Find an…

A: Solution

Q: The strength of a weld is determined by the formula X = O + 3N + 5C where X is the strength, and O,…

A: Given,μo = 0.1665μN = 0.0455μc = 0.0346σo = 0.0340σN = 0.011σc = 0.0131X = 0 + 3N+5Ca) ∈(X)…

Q: coin with two sides - H and T, 6 times. Suppose the probability of getting a heads is 1/3. Let…

A: It is an important part of statistics. It is widely used.

Q: 11. Suppose X and Y are random variables, c and d are constants. What is E(CX - DY)? OA. E(X) - E(Y)…

A: Let E(X) be the expected value of X and E(Y) be the expected value of Y. Note : Since you have asked…

Q: 2)Consider a random variable X with MGF M(t) = e³t+4t² Find the mean and variance of X.

A: Question 2)The moment generating function (MGF) of a random variable is, The objective is to…

Q: 3. Suppose that X - N(3.2, 6.5), Y ~ N(-2.1, 3.5), and Z ~ N (12.0, 7.5) are independent random…

A: Given X~N(3.2, 6.5) and Y~ N(-2.1, 3.5) and Z~N(12,7.5) Note: according to the Bartleby, expert…

Q: 5. Suppose that X and Y are two independent discrete random variables, where X and Y only take…

A: Independent events: Two or more events are said to be independent if occurrence of one does not…

Q: 4.62 If X and Y are independent random variables with variances o = of the random variable Z = -2X +…

A: 4.62: Given that X and Y are independent random variables with variances σX2=5 and σy2=3. And σXY=0…

Q: 2. If X, Y are independent random variables show that variance (X-Y)= variance (X) + variance (Y).…

Q: Which of the following statements are true about the sum of discrete, independent random variables?…

A: Given the two discrete independent random variables and want to comment on the sum of two…

Q: Let Y₁, Y₂, and Y be independent, identically distributed random variables from a population with…

A: Dear student, If you find this solution helpful please upvote it. The solution is given below :

Q: The strength of a weld is determined by the formula X = 0 + 3N + 5C where X is the strength, and O,…

A: X is the strength of the weld, where O is the oxygen weight percent in the weld N is the oxygen…

Q: 0.9301 0 8943

A: To find the approximate value of z

Q: Given that P(A|B) =0.5, P(A) = 0.4, and P(B)3D0.44, then P(BIA) is equal to:

Q: Let X1, .., X10 be i.i.d. Bernoulli(p) random variables. Find the most powerful test of size a =…

A: We are given the following: Xi~Bernoulli(p) i=1,...10the pmf of X is as followsPX=x=px1-p1-x…

Q: Suppose X, Y, and Z are three independent normal random variables. X has an expected value of -7 and…

A: Given information: T=2X+4Y+7Z Consider, ET=E2X+4Y+7Z =2EX+4EY+7EZ =2*-7+4*-9+7*8…

Q: m varia bies 10, 0x2 correlation between 'U' and 'V' is zero, when U = 3 X + 4 Y and V = 3 X- Y.

Q: Variable Mean(Expected Value) -8 Standard Deviation 1.5 0.3 1.1 Coefficient 3 -4 -2 a) What is the…

A: Comment: As per the our company guidelines we are supposed to answer only three subparts. Kindly…

Q: A9. Let X and Y be independent standard normally distributed N(0, 1) random variables. What is…

A: Given that X and Y are independent standard normal distribution N(0 , 1).

Q: For any two random variables Y₁ and Y₂, Var(Y₁Y₂|Y₁ = y₁) = y{Var(Y₂|Y₁ = y₁). TRUE

A: Given that Y1 and Y2 are two random variables. Formula: If X is a random variable, then VX=EX2-EX2.…

Q: 14. Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable…

A: The random variable y be the annual return for the Vanguard Balanced Index.

Q: The cdf of a random variable Y is |1– exp(-0.4y), y 20 F,(y) otherwise Valuate P{2.5 <Y < 6.2}.

Q: Find the value of t if P(Z > 1) = 1000

Q: A discrete random variable X can take 3 outcomes: 0,1 and 2 with probabilityP(X = k) = c(k + 1)2, k…

A: It is known that the random variable X takes 3 outcomes: 0,1, and 2 with the corresponding…

Q: We have the following information about the random variables X and Y: |x=2, |y=−1 , ox = 0.25, c X…

A: a)It is given that, .

Q: If W is the Gaussian (82, 7.2) random variable, calculate the following: P(W60) c. P(W<87)

A: As per Bartleby guideline expert have to answer first question three subparts only dear student…

Q: 4. Suppose X and Y are independent random variables such that E(X) = 0, 6, E(Y) = -1, Var(X) = 1,…

A: 4. The given value are EX=0,EY=-1,VarX=1,andVarY=4.

Q: (Q2) Suppose Y₁,..., Y, are mutually independent random variables such that for a given Xi…

A: (i) To find the 95% confidence interval for ß, we use the formula:\[ \hat{\beta} \pm…

Q: Let X be the Random Variable: x | P(X = x) 0.5 0 1 0.2 2 0.3 Let X1, X2 be the identically…

Q: Suppose X is a random variable with X - N(90, 52) and let u = the mean of X me = the median of X mo…

A: Solution

Q: (a) The correlation

A: Answer:

Q: Let X1, X2, ., Xn be a random sample from a distribution with mean u and variance o2. Consider the…

Q: Q1) Let X denotes the minimum of the two numbers that appear when a pair of fair dice is thrown…

A: The sample when a pair of dice is rolled is given as below: S = {(1, 1), (1, 2), (1, 3), (1, 4), (1,…

Q: c. Suppose that the random variables X1, X2 and X3 are independent with means and variances as…

Q: If X and Y are independent random variables with X~N(2,32) and Y~N(1,42), find P(X<Y). (You need to…

Q: Let X and Y be two random variables. Suppose we know E(X) = 7 and E(Y)=3. Let Z = X − Y be a random…

A: Given EX=7 and EY=3.Let Z=X-Y.Then,E(Z)=4

Q: Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a]…

A: The given information is :For random variable X:Variance (Var[X]) is 4.8.For random variable…

Q: 2x + 1 25 b. P(X ≤ 1) d. P(X> -10) 3.1.11 WP SS a. P(X= 4) c. P(2 ≤X <4) vs f(x) = x = 0, 1, 2, 3, 4

Q: Page 143, 2.6.6*. Let X₁, X₂, and X3 be three random variables with means, variances, and…

Q: Suppose that X is a random variable for which the m.g.f. is as follows: M(t) = 1/4(3et+e-t), -∞<t<∞…

A: We can get the mean and variance after finding the first and second derivative of mgf at t= 0

Q: Let X1, X2,...,X3 denote a random sample from a population having mean u and variance o2. 302 Which…

Q: If U and V are two independent standard normal random variables and Z=0.6U+0.8V. Determine Corr (U ,…

A: It is given that, U and V are two independent standard normal random variables i.e. U~N(0,1) and…

Question

5.6.1 X and Y are independent, normal random variables with
E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.
Determine the following:
a. E(3X+2Y)
c. P(3X + 2Y < 18)
b. V(3X+2Y)
d. P(3X + 2Y < 28)

Expert Solution

Step 1: We have given that

E(X)=2, V(X)=5, E(Y)=6, V(Y)=8

X and Y are independent then Cov(X,Y)=0

Note: According to bartelby question answer guidelines an expert can solve only three subpart of one question rest can be reposted.

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Really need it to study, please don't copy the answers from others.
q13- X and Y are two independent random variables. We know V(X) = 26.43 and V(Y) = 23.67, then V(8X + 5Y) is: a. 862.68 b. 2283.27 c. 329.79 d. 16490.91
How were the correct answers of 1/45 and -2/73 attained?
Ee.6.
2. If X is a normal random variable with mean u 3 and variance o2 16, find P{X-1 }
Let Y1 and Y2 be independent random variables with unknown mean μ and known variance σ2 =1. Which of the following two estimators of μ has smaller MSE? Justify your answer.
Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)
[8.3]
Suppose X and Y are independent random variables such that E(X) = 0, -1, Var(X)= 1, and Var(Y) = 4. Find the following: a. E(7X + 2Y – 3) b. Е(X?) с. Var(2X — 5Y + 7)
Solve by SPSS
Suppose X, Y, and Z are three independent normal random variables. X has an expected value of -7 and a standard deviation of 1.6; Y has an expected value of -9 and a standard deviation of 1.8; Z has an expected value of 8 and a standard deviation of 1.4 Let T = 2X + 4Y+7Z Variable Mean(Expected Value) Standard Deviation Coefficient X Y -7 -9 1.8 4 1.6 2 Z 8 1.4 7