Answered: 3. The expection of a random variable X…

3. The expection of a random variable X is equal to 5. What can be say about the expectations of (a) (b) In X (c) X² + 5X – 3?

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: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

Q: 3. Consider a share that is modelled by a binomial random variable. The probability that the share…

A: Given data consider a share that is modelled by a binomial random variable

Q: In a class of 8 students, what is the probability that at least one was born in July?

A: c) Given that there are 12 months in a year. The probability that student born in July is…

Q: If X is a random variable with probability distribution as given below: X P(X) 0 1 2 3 k 3k 3k k…

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Given that, E(X) =-9 , E(Y) =-5, E(Z) =-1 Var(X) =3, Var(Y) =1, Var(Z) =34

Q: Example 2.15. Let X be a random variable with the following pdf: + 1. Find its CDF. 2. Evaluate the…

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Since, you have you have posted a question with multiple subparts we will solve first three subparts…

Q: 1. Decision Theory Consider the following random variable X. For positive integers k, Pr[X = 2k] =…

Q: 4. Let X be a discrete random variable with E (X) = 3 and Var(X) = 0.5, What are the mean and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: $ Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on…

A: Given EX=-5,EY=6,EZ=3 and VarX=15,VarY=10,VarZ=29.

Q: (1) Let X be a random variable with a function [A(3x² +6) -1,0,1,2 . then (0) k = (6) k = (e) * (d)…

Q: 2,...,A3 a populati ng meanu and variance Which of the estimators have a variance of u? X1+X2++X7 7…

A: Solution

Q: Suppose that X, Y, and 2 are jointly distributed random variables, that is, they are defined on the…

A: Given that E(X)=-8E(Y)=6E(Z)=-1Var(X)=33Var(Y)=25Var(Z)=48

Q: 11. Let X be a random variable with the following probability distribution: t X f(x) -3 6 2 9 T 3…

A: From the provided information,The probability distribution is as follow:x-369f (x)1/61/21/3

Q: Let X be a discrete random variable. (i) Prove that V ar(X) = E(X2) ? (EX)2. Hint: Use the…

A: We want to prove both results

Q: uted random variables, that is, they are defined on the same sample space. = 5 )=26 Dw.

A: According to guidelines we solve first three subparts when given multiple subparts.

Q: 1-4x and 4 1+3x 1-x 1+2x (5) If a random variable assumes 4 values with probability the 4 4 4…

A: If the random variable assumes 4 values , then the sum of all probabilities for x should be equal to…

Q: 4. The probability function of a d.a.d. X is: img. The expected value of X is E(X)= ? The…

A: Given function is f(x)=2x+125 ; x=0,1,2,3,4

Q: (2) Let X be a random variable with p.d.f. 1<x<10 f(x) = then o.w 3 (a) k=2 (b) k=8 (c) k = (d) k=3…

A: Solution: 2. From the given information, the probability density function of X is

Q: 5. Let the random variable X be the number of days that a certain patient needs to be in the…

A: Let x be the number of days that a patient needs to be in the hospital.Its PMF is given byConsider…

Q: 2. Which one of the following statements is true for all random variables X? ?X E(X?) > Var(X).…

Q: 3. V, W, X and Y are independent random variables, each having a normal distribution. V has mean 4…

Q: 2) Suppose Y = 3(X - 1)? where X is a random variable that takes on values 0,1, & 2 with probability…

Q: If X is a binomial random variable, for what value ofθ is the probability b(x; n, θ ) a maximum?

A: The value of q is given below:

Q: 3. The following table shows the probability distribution of a random variable X. X 2 5 8. 10 3 5 7…

A: We want to find A) E(X) and Var(X) B) E(8X+3) and Var(8X+3)

Q: Parts A and B

A: The probabilities are listed that were presented by the prosecution for the known characteristics of…

Q: 5. The random variable X represents the number of cherries in a cherry puff, and has the probability…

A: Solution

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor Therefore, X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: 7. Suppose X and Y are independent random variables. Y a. What is the correlation coefficient of X…

A: X and Y are independent random variable. So, Cov(X,Y) = 0 a. We need to find the correlation…

Q: If X Z N(5,4), then what is the probability that 8 < Y < 13 where Y = 2r +1?

A: Solution: Let X~N(μ= 5, σ2= 4)

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that X is a continuous random variable that takes on values between 10 and 40, then…

Q: Let X be a random variable. Which of the following statement is INCORRECT? If V (X) = 0, then there…

A: In statistics random variable is a variable whose value will be defined on the basis of a random…

Q: (3) Let X be a random variable with p.d.f 3x* + 6x) 0<x<l , then E(4x) is (12 12 (c) (d) 12 (b) (e)…

A: Wehave to find the Expectation E(4x) of a random variable X with the given pdf.

Q: (a) The correlation

A: Answer:

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Given Information: Consider X, Y and Z are jointly distributed random variables. Consider the…

Q: If ô, and @2 be two unbiased estimators of 0 with variances oỉ and o, respectively. What is the…

A: To obtain minimum variance, we will diffrentiate the variance of the unbiased estimator then equate…

Q: Let X be a random variable having p.d.f. fx(x) = cx², -2 < x < 2. For the following parts, your…

A: Given density function: fx=cx2, -2<x<2 c value: ∫-22fxdx=1 from the total probability…

Q: Let X be a random variable with probabilities as shown in Table 3.7. Table 3.7 Values of X and P(x)…

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

Q: 3. The following table shows the probability distribution of a random variable X. BREED 8. 10 3 7 1…

A: E(X)=∑xP(x)

Q: Let X be a discrete random variable with the following pmf: 10 15 21 28 p(x) | 8-c 4.c 9-c 10-c 5.c…

A: It is given that, P( X≤ 2 ) = 0.24. That is, P( X≤ 2 ) = 0.24 P(X=0)+ P(X=1 ) = 0.24 8c+4c = 0.24…

Q: Many people believe that the daily change in price of a company's stock in the stock market is a…

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

Q: The PMF of the number of components K of a system that fails is defined by PK (k) = {() (0.2)*(0.8)…

A: Solution-; Let, K=be the number of components of system that fails Given: The pmf of K is,…

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: GivenE(X)=5E(Y)=-7E(Z)=3Var(X)=20Var(Y)=6Var(Z)=23

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

100%

3. The expection of a random variable X is equal to 5. What can be say
about the expectations of
(a)
X+3
(b)
In X
(c)
X² + 5X – 3?

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

5. The random variable X, representing number of errors per 100 lines of software code, has the following probability distribution: 3 4 6. f(x) 0.05 0.23 0.4 0.02 0.3 Find the mean of g(X) given g(X) = (2X – 5)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-1 E(Y) = 4 E (Z)=0 Var(X)=20 Var(Y) = 27 Var (Z) = 38 Compute the values of the expressions below. E (5Z-2) = 0 2Z+X -5 Var(2X-3) = 0 E = E (32²) = 0 Explanation Check X O hp Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Term
1. Suppose a discrete random variable Xhas probability function given by 5. 10 12 0.13 POX-1) 0.08 0.16 025 16 2y 0.03 005 Solve for y andfind the mean and variance of X.
Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7
B5. Let X₁, X₂, ..., Xn be IID random variable with common expectation µ and common variance o², and let X = (X₁ + + X₂)/n be the mean of these random variables. We will be considering the random variable S² given by (a) By writing or otherwise, show that S² (b) Hence or otherwise, show that n S² = (x₁ - x)². = Ĺ(X₂ i=1 X₁ X = (X₁-μ) - (x-μ) = Σ(X; -μ)² - n(X - μ)². i=1 ES² = (n-1)0². You may use facts about X from the notes provided you state them clearly. (You may find it helpful to recognise some expectations as definitional formulas for variances, where appropriate.) (c) At the beginning of this module, we defined the sample variance of the values x₁, x2,...,xn to be S = 1 n-1 n i=1 ((x₁ - x)². Explain one reason why we might consider it appropriate to use 1/(n-1) as the factor at the beginning of this expression, rather than simply 1/n. B6. (New) Roughly how many times should I toss a coin for there to be a 95% chance that between 49% and 510/ of my nain toon land Honda?
D1. Account
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
I am really having a difficult time with this problem can you please do it step by step so I can see how you did the calculattions and can you label them as well. Can you please do this step by step and label it .
Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27
(3) Let X be a random variable with p.d.f 2 (3x+6) 15 then E(x) is 11 12 (b) 30 (c) 30 (d) (e) None of these 33 716
Example 2.14. Show the CDF of the random variable X with the following pdf: Sx(2) = lwa(x) Example 2.15. Let X be a random variable with the following pdf: 1. Find its CDF. 2. Evaluate the following probabilities using its CDF and/or pdf. a) P(} 1) c) P(X > }|X < 1)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y) = 4 Var(X) = 24 Var(Y) 18 Var(z)=7 E(X)= -3 E(Z) =-1 Compute the values of the expressions below. E(-4-5X)= 0 %3D ? ()- 0 Var(-3+2.X) = 0