Two independent random variables X and Y uniformly distribution on the interval [0,4]. The expectation of Y, given that at least one of the RVs is less than 1 is: Select one: а. 1.61 b. 2.12 С. 1.1 d. 1.36 е. 1.25

Two independent random variables X and Y uniformly distribution on the interval [0,4]. The expectation of Y, given that at least one of the RVs is less than 1 is: Select one: а. 1.61 b. 2.12 С. 1.1 d. 1.36 е. 1.25

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: A taxi service receives an average of 8.8 calls a day from customers who need a ride to the airport.…

A: Solution: Date:16-2-2022 As per bartleby policy i answered only…

Q: А. 1/4 В. 5/8 С. 7/8 D. 3/4

Q: How would we start with finding the conditional distribution of (x1, x3)T? We are given the info…

Q: 11. The joint probability distribution of the random variables X and Y is f(x, y). Find the…

A: Joint probability density function explain the probability occurrence of two variance. Marginal…

Q: If "X" is Poisson yandom variable with pavametev u = 3, find the pro babilities for X= 0, 1,2, ?3,4…

A: Given: Poisson parameter = u= 3 to find: probability when x=0,1,2,3,4 or more

Q: Let X be a random variable uniformly distributed over (-1,1) and Y =X². Find p(x,y) Select one: а.-1…

A: Let X be a random variable. In the given scenario, the random variable X is uniformly distributed…

Q: For a uniform random variable X - U(20, 26), find x0.6: (Round the answer to 4 decimal places) X0.6

A: It is given that, X~U(20,26) f(x) =1/(26-20) = 1/6 ; 20<x<26 We have to find x0.6 i.e. 60th…

Q: [10] The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~…

A: In this problem, a random variable Y is described to follow a normal distribution with a mean of 30…

Q: A continuous random variable X is uniformly distributed over the interval [10, 16]. The expected…

A: Given that, X follows uniform distribution [10, 16]

Q: Given a random variable X, we consider the probability that the distance between X and its mean is…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: Suppose the joint PMF of the random variables X and Y is P(X= x, Y = y) = a(x+y) 0 1. Find the value…

A: the joint PMF of random variables X and Y is:- P(X=x,Y=y) = a(x+y); { (x,y) : {4,5,6} x {1,2,3} }…

Q: The expected values E[5Y1(Y2 )2- 3Y, + 7] is

A: Here given EY1 = 3VY1 = 4 EY2 = 2VY1 = 6& Y1 , Y2 are independentVY1 = EY12 - EY12∴ EY12 = VY1…

Q: 1. The percentage of defective articles produced by a machine is 8%. Use a suitable approximation…

A: Let there are n trials and each having two outcomes - Success and Failure. The trials are…

Q: . The average amount of calories in a box of cookies is 120 calories. A person thinks this number…

A: Given' Average amount of calories in a bag cookies is 120 calories A person think (claim) that this…

Q: 12. Suppose that X is a random variable for which the m.g.f. is as follows: V(1) = (4 + e' +e) for…

A: The random variable X has a moment generating function ψ(t)=164+et+e-t for -∞<t<∞ We…

Q: Q2) Generate 3 Gamma probability distributions of continuous random variable Z with (a = 1ẞ= 1), (a…

A: The Gamma distribution is a continuous probability distribution commonly used in various fields such…

Q: Given n independent binary variables X,,X,...,X,, that can take the values of 0 or 1, are…

Q: Find the marginal distributions of the X and Y random variables. Find the conditional distribution…

A: Given a joint probability distribution , we need to find marginal distributions and conditional…

Q: Let X1, X2, ...X, be an i.i.d. N(1, 202) sample. (1). Write down the likelihood function for the…

Q: Let X₁, X₂ be independent random variables with mean and variance o, and a is a constant. We also…

A: Given that X1,X2 be independent random variables with mean μ adn variance σ2. So, E(X1)=μ=E(X2) and…

Q: Show that, if X1 and X2 are independent random variables with geometric distributions of a parameter…

Q: Q 6.1. Suppose Z = (Z1, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i≤ 3,…

A: Given that be a standard multi-variate Gaussian random variable.For are i.i.d. random variables.

Q: Q3: Let X, X2...X, be a random sample from a Poisson distribution with mean 8. The sequential…

A: Please note that as per our guidelines if multiple questions are posted, we can answer the first…

Q: Let W1 and W2 be independent geometric random variables with parameters p1 and p2. find: a)…

A: W1 & W2 are independent geometric random variables with parameters p1 and p2 First we will take…

Q: Describe the distribution of the random variable S = n . Identify the mean and variance of this…

A: Given that Xi follows Bernoulli distribution with parameter θ, i = 1,2,.......n Note : According to…

Q: N(u = 0, 02 = 4), Y2 ~ N(µ = 3, o? Consider the three normal random variables Y1 Y3 ~ N(u = -3, o² =…

Q: c) P(2 1)

Q: 1) Assume that a random variable Y has Weibull distribution with parameters a=2 and B=5. a) Find…

A: Given information: A random variable Y follows a Weibull distribution with parameters: It is…

Q: A transmitter sends out a random number X which can take values of -1, 0, or 1, each with…

A: X can take the values of -1, 0, or 1, each with probability 13. So, the PMF of X is P(X=x)=13,…

Q: True or False (h)__________ If X and Y are independent, then 300(X) and 300(Y) are dependent. (i)…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: Find the mотеnt m,:

Q: Let X and Y be random variables with joint distribution pxy(:) given by the following table. Pxy X =…

A: Given Information: X and Y are random variables. The joint pdf is given. Determine the marginal pdf…

Q: Consider a random variable that is normally distributed where u = 40, o = 4, and x = 50. find the…

A: According to the given information, we have Mean = 40 Standard deviation = 4

Q: Exercise 4 Show that if X ~ Fp.g, then the corresponding probability density function is: r() x-1…

Q: 1. Let the moment generating function of random variables X and Y be e and e" respectively. Let Z =…

A: Let X be a random variable. The moment generating function of X is denoted by MXt=EetX. Then, the…

Q: Given X ~N (25, 52) Find k such that P(20 < x < k) = 0.4 using normal distribution laws

A: Solution-:Given: We want to find k such that,P(20<X<k)=0.4

Q: 4 -3 01 ΗX~N, (μ, Σ) and μ = 2| E =|-3 6] 5] a) Specify the distribution of b) If Y, = 3X1 – X2 and…

A: Given , X ~ N3(µ, Σ) Here, μ is the mean vector and Σ is the covariance matrix. The mean vector and…

Q: A random variable X ~ U[−3, 5]. Find P(4X – 7 > 1). O 0.833 O 0.625 O 0.375 O 0.450 O 0.500 No…

A: given data X~U[-3,5] uniform distribution P(4x-7>1) = ?

Question

Two independent random variables X and Y uniformly distribution on the interval [0,4]. The
expectation of Y, given that at least one of the RVs is less than 1 is:
Select one:
а. 1.61
b. 2.12
С.
1.1
d. 1.36
е. 1.25

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 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

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

iid 1. Let T1,T2, ..., n) = p · (1 – p)"-' I{1,2,...}(n). (That is, N ~ geom1(p).) What is the distribution of елp(rate A) and let N be an independent random variable with P(N = T = T1 +T2 + .+TN? (Name it!)
A normally distributed random variable X characterized with u? = 16 and o = 5. Find а. Р(3 0} с. Р(]Х — 4|> 7}.
2. The distribution of a random number X is Uni(0, 1). Find the probability that (a) the first decimal of √X is equal to 3. (b) the first decimal of X² is equal to 3.
For E (0,1) let Xp be a Geometric random variable with parameter p. (a) Find a value of p so that P(Xp> 2.5) = 9. (b) Let An be the event that Xp is even. Determine P(A,) in terms of p. (c) Suppose Y, is a random variable which is equal to the remainder after integer division of X, by 3. Let p = i, and determine the conditional probability mass function of conditioned on the event Yı = 1.
A continuous random variable X is uniformly distributed over the interval [12, 18]. The variance of X isA. 15B. 6C. 3D. 9
Two independent random variables X and Y uniformly distribution on the interval [0,5]. The expectation of Y, given that at least one of the RVs is less than 1 is: Select one: а. 1.61 b. 1.25 С. 1.36 d. 2.12 е. 1.1
3. If X;~N(0,1), i = 1,2,3,4 are independent Normal random variables and Y is given as Y =(X,+X,)' +(X, + X,)' . If aY~x², . find the constant a. 2
10. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.
Two independent random variables X and Y uniformly distribution on the interval [0,3]. The expectation of Y, given that at least one of the RVs is less than 1 is: Select one: а. 2.12 b. 1.25 С. 1.1 d. 1.36 е. 1.61
Q6. In the following diagram: Họ: µ = 4 ; H1: µ= 1. f(X) Ho Xp Rejection region Non-rejection region Examine the probabilities represented by the regions, a,b and c. Identify the incorrect statement: A. a = Pr(Type I error 'AND’ Not-Type II error). B. a +b = Pr(Type I error). С.с 3D Pr(Туpe Il error). D. a + b + c = Pr(Type I error 'OR’ Type II error) %3D A. A В. В С. С O D. D
Q 6.1. Suppose Z = (Z1, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i ≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)-(d), on the left is equal in distribution to exactly one random variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. (a) (X₂) (¹) (X) = (2) 1/√2 (Ⓒ) (x₂) - (3/1² ¹1/1²) (2) (c = 2 0 = 2 Z₁ 1) (²) 3 (4¹) (X) = (²¹) (1) (2) (3) Y₁ 1 (29) - ()) (2) = Y₂ 1 Y₁ (121) = (1/² √₂) (2) (1/√2 1/√2 /2 −1/√√2, Y₂ X₁ X₂ = 22 1 1 2 0 Y₁ 2 1 (4) (2)) = (²) (²) 1 1 Z₁ Z₂ Z3
None