Q15. The random variables X,Y each take only the values 1 or 2. i. When they have a following joint mass function, what is P(X=2 | Y=1) ? |Y=1 |Y=2 |X=1 1/3 1/6 ii. When they have a following joint mass function, what is E(Y)? Y=1 |Y=2 X=1 1/6 1/3 X=2 1/6 1/3 X=2 1/6 1/3

Q15. The random variables X,Y each take only the values 1 or 2. i. When they have a following joint mass function, what is P(X=2 | Y=1) ? |Y=1 |Y=2 |X=1 1/3 1/6 ii. When they have a following joint mass function, what is E(Y)? Y=1 |Y=2 X=1 1/6 1/3 X=2 1/6 1/3 X=2 1/6 1/3

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: Q-2: Let X1, X2, ..., X, be independent, exponentially distributed random variables with mean ). 1.…

Q: Suppose for a certain random variable, X, we have V( X) =1. then which of the following is a true…

A: For a certain random variable, X, we have V(X)=1.

Q: Compute the probability P(Y= k), where is a positive integer. Your answer can include the variable…

A: From the given information, X is a uniformly distributed random variable on (0, 1). Y is geometric…

Q: be a bivariate gaussian random vector with 16 and p= 0.7. %3D

Q: B. Let X and Y be random variables and let A e B. Prove that the function

A: SOLUTION ;

Q: d. Find Ox Find E[Y2] Find oy e. f. g. Find Var[X + 3Y - 6]

Q: Suppose that X and Y are discrete random variables taking the values 1 and 2. Suppose further that…

Q: 8. Let X be a random variable from a distribution with density g(z) = ne nla-m)1jm(x). ind the…

Q: Let X; be independent Uniform(-5,5) random variables, for i=1, 2, ..., 14. Let Y=X₁+X₂+...+X14. (b)…

Q: i) Find the value of k which make the following function a pdf (15 y 64 64 3 + ky 0<ys3 - 2 sys0 r)…

A: The probability density function (pdf) gives the probability at each possible value a continuous…

Q: The means, standard deviations, and covariances for random variables X, Y, and Z are given below.…

Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |(ry² + x²y), if 0 < 1< 1,…

A: The joint pdf of two random variable x and y is given: fX,Yx,y = cxy2 + x2y,if 0≤x≤1, 0≤y≤1…

Q: 10. Let X, Y be random variables. Suppose thatA IS exponentially distribi 1. Given X = 1, Y is…

A: As X~ Exp(1) and Y/X=x ~ U(x, x+2) Answer : E(Y) = 2

Q: What is the expectation (to 2 decimal places) of Y? ELY

Q: 11) Consider the following joint probability mass function (PMF): f(X,Y)= kxy2 s= {(1,1), (1,2),…

A: Conditions for discrete probability distribution: The following requirements should be satisfied for…

Q: Let the following simple random sample X1, X2, X11 following: 1. Binomial pmf. (11, ¾); 2. Uniform…

A: The pmf of discrete uniform distribution is given by p(y)=1n=111 The cdf of discrete uniform…

Q: Let zand y be two independent Gaussian random variables, both with expected value zero and variance…

A: Given, x and y be two independent gaussian random variables. We have to find the power spectral…

Q: Find (d) E (X² . Y²)

Q: A statistician takes the same bus to work every day. He arrives at the bus stop at 8AM every…

Q: h. Find Var[3X - 2Y+ 35] i. Find E[(2X - 8)/5] j. Find Var[(2X - 8)/5]

A: Given E(X)=4, E(Y)=6, V(X)=<<84, V(Y)=54,

Q: Suppose that the random variables Y1, . , Yn satisfy Y, = B ; + e, i= 1,..., n, where #1, ..., In…

A: From the given information, Y1, Y2,....,Yn satisfy Yi=βxi+εi, i=1,2,....,n. Here, x1,x2,....,xn are…

Q: 8. Let X and Y be random variables and let A e B. Prove that the function X (@), if w e A, Y (@),…

Q: .Given that (x, y) = (x+2y)/k if x = -2,1 and y = 3,4, is a joint probability distribution function…

A: Note: Hi! Thank you for the question, As per the honor code, we are allowed to answer three…

Q: The joint PDF of X and Y random variables is given below. The constantc can be found as fxx(x, y) =…

A: Solution

Q: Find the mотеnt m,:

Q: A discrete random variable has the p.mf f(x) = ax x=1, 3, 5 O A. 0.11 O B. 9 OC. 4.5 O D. 5

A: Given data: f(x) = a.x Where , x = 1,2,3 To find : value of a

Q: 1. Given the probability mass function of a discrete random variable X Scx2, if x = -1, 1, 2, 3, 0,…

A: Properties of probability mass function: Total probability should be 1. The probability values…

Q: A survey shows the following results: n = 50 where 32 subjects have a Facebook account, 20 subjects…

A: Obtain the probability of no Facebook. The probability of no Facebook is obtained below as…

Q: Let X and Y be two random variables and E(Y) 1. Which one of the following is true about E(Y|X)? a.…

A: Solution

Q: Let X and Y be two independent exponential random variables. X ~

A: Given, X and Y be two independent exponential random variables. X~exp(1) and…

Q: ke-3x Let f(x)= 0 < X < 0 %3D be pdf of the random variable X. otherwise

A: Given,f(x)=ke-3x ;0≤X≤∞0 ;otherwise

Q: X and Y are independent random variables with PDFS (1 e~x/3 3 1 e-y/2 2 fx(x) : x 2 0 , fy(y) : y >…

Q: The PDF of random variable W is c(w + 5), -5 <w < 7 fw (w) %| 0, otherwise

A: Given,f(w)=c(w+5); -5≤w≤70; otherwise

Q: Q4/ a. Find areal root of the equation f(x) = e* - 2 = 0 (Using False Position Method in four…

A: Solution:- Question 4(a) Here , ex-2=01st iteration :Here f(0)=-1<0 and f(1)=0.7183>0∴ Now,…

Q: 14. Let X be a discrete random variable with the following PMF 1 for k = -2 4 1 for k = -1 Px (k) 1…

A: Farmula used Range=Maximum-Minimum

Q: For two random variables X andY the following information is given. V(X)=3, V(Y)=2 and cov(X, Y)=…

A: The provided information are: V(X) = 3, V(Y) = 2 and Cov(X,Y) = -1

Q: The joint p.d.f of a two-dimensional random variables (x, y) is given by f(x,y) = kxe , 0 0 = 0 ,…

A: To find k, we need to apply total probability =1.

Q: Let X, (i 1,.,n) be a random sample from the N(4,02) population with unknown ameters u and o2. Then…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: The PDF of a random variable Y is y/2 0<y<2 fy (y) otherwise a. What is E[Y]? b. What is Var[Y]?…

A: The PDF of random variable Y is f(y) = y/2 , 0<y<2 , 0 otherwise

Question

Q15. The random variables X,Y each take only the values 1 or 2.
i. When they have a following joint mass function, what is
P(X=2 | Y=1) ?
|Y=1
Y=2
X=1
1/3
1/6
ii. When they have a following joint mass function, what is E(Y)?
|Y=1
Y=2
X=1
1/6
1/3
X=2
1/6
1/3
X=2
1/6
1/3

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

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

+
The random variables X, Yeach take only the values 0 or 1. Their joint mass function is
given in the table below.
Y=0
Y=1
What is
i.
ii.
111.
P(X=0 | Y=1)
Cov(X, Y)
Cor(X, Y)
X=0
5/12
1/6
X=1
1/6
1/4
0

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Let X1,..., X10 be a random sample of size 10 from a N(u, o²) population. Suppose 10 Y =(X; - 4)? i=1 Find the probability that the random interval Y Y 20.5' 3.25 includes the point o?.
Q. Fourteen (V, X) : There are no correlated random variables X,Y with a? = 2a where Corr(X,Y) = a
Please answers the last three questions The random variables ξ, ξ1, ξ2, . . . are independent and identically distributed with distribution P (ξ = 0) = 1/4 and P (ξ = j) = c/j for j = 1, 2, Let X0 = 0 and Xn = max(ξ1, . . . , ξn) for n = 1, 2, . . .. What value must c take? Explain why {Xn, n = 0, 1, 2,..... } is a Markov Write down the transition Draw the transition diagram and classify the states (aperiodic, transient, re- current, eorgodic, etc). Calculate P (Xn = 0). Calculate P (X4 = 3, X2 = 1|X1 = 3).
. Let X and Y be random variables and let AE B. Prove that the function X(w), if we A, Y(w). if w€ AC is a random variable. Z(w) =
Chapters: Normal and Exponential random variables. Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.
We have the following information about the random variables X and Y: 4 8 11 4 5 ox = o Cov(X, Y) 225 15 75 225 Calculate the standard deviation of Z 3Y — Х. oz
The joint p.d.f of two random variables X and Y is given by 1. ƒ(x, y) = = x(x − y),0 < x < 2,− x < y
Kelvin’s bookcase holds 2 algebra books, 1 calculus book, and 4 geometry books. Books are taken at random from his bookcase, one after another and without replacement, until a geometry book is had, at which point no more books are taken. The random variable Y represents the total number of books taken during this experiment. Find Pr[ Y = 3 ].
Suppose that X1, X2, ..., Xn is a random sample with a probability law P(x) = {0x, 0 Where 8 is an unknown parameter. si x = 1,2,3, 4; otherwise A. Get an estimator of 0 by the method of the moments. B. Prove that the estimator is unbiased.
Answer accurately.
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. X₁ (a) X₂ (b) (x₂) - (2) (c) (x²) - (¹/1² 1/√²) (2₁) (3/√2 = √2 = (V2) Z₁ (d) (x) - (1) (²) X2 Y₁ (9)-(-) (2) (1=1) Y₂ (1) Y₁ (²) (4) - (1/² (3) (1/√√2 1/√2-1/√2) (x₁) = (²₁ ² ✓/³²) (3) 2 2 √2 1 Z3 Y₁ → ()-()) (4) = Y₂ 1/2) (2) 1) (2)
Let X and Y be jointly normal random variables with parameters µx = -1, ož = %3D 4, μΥ1, σ 1 and ρ 5 a. Find P(X + 3Y < 4). b. Find E (X²Y²)