A random variable X~Binomial (2,1/3) is chosen, but the result is badly recorded; the record Y has an equal chance of being X, X+1, X+2. a. Find the joint PMF of X and Y. Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=2 b. Find the conditional PMF of X given Y Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=2 c. The Y=2 column of your second table should match the marginal distribution of X (if it doesn't, check your answer). What does this say about how useful a record of "Y=2" in telling you the actual value of X?

A random variable X~Binomial (2,1/3) is chosen, but the result is badly recorded; the record Y has an equal chance of being X, X+1, X+2. a. Find the joint PMF of X and Y. Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=2 b. Find the conditional PMF of X given Y Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=2 c. The Y=2 column of your second table should match the marginal distribution of X (if it doesn't, check your answer). What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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: Assume that X and Y are two random independent random variables with mean 2 and 3 and variance 2 and…

Q: 6.49 Let Y₁ be a binomial random variable with n, trials and probability of success given by p. Let…

A: Given: Y1~Bin(n1,p) Y2~Bin(n2,p) Y1 and Y2 are independent. The value of PX=x=nx×px×qn-x Also,…

Q: We are given Z as a random variable with E(Z) = 9 and Var(Z) = 5. Solve for the following: (show…

Q: Given independent random variables with means and standard deviations as shown, Mean SD X65 20 Y45…

A: Given independent random variable with the mean and standard deviation as shown below, Mean,…

Q: When X is a binomial random variable, then the probability X = r successes can be found using the…

Q: 2. Suppose that X is a random variable with E(X) = 6 and Var(X) = 4. Find the following: a) Е(4X +…

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: Write a program to generate two independent and uniformly distributed random variables x₁and…

A: It is given that the random variable X follows Uniform distribution with parameters a (min)=-1 and b…

Q: Let X be a random variable from a Chi-Square Distribution with 13 degrees of freedom. Jada is…

A: Let X denotes the random variable from chi square distribution with 13 degree of freedom Y=a+bx…

Q: Let X1 and X2 be two independent normal random variables with parameters (0,1) and (0,4)…

A: X1 and X2 are two independent normal variates mean and variance (0,1) and (0,4) respectively. Then,…

Q: Three components are randomly sampled, one at a time, from a large lot. As each component is…

A: The objective of this question is to find the mean (μx) of the number of successes when three…

Q: Suppose the joint PMF of random variables X and Y is P(X = x, Y = y) =   …

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

Q: 3. If X and Y are 2 random variables such that Y = ax + b, then the variance of Y is O A. aVar(Y)…

A: Note According to Bartleby guidelines expert solve only one question and rest can be reposted.

Q: There are three random variables X, Y and Z,for which we know the following information E(X)= 6,…

A: Given,V(X)=18 , V(Y)=22 , V(Z)=4Cov(X,Y)=-12 , Cov(X,Z)=5Cov(Y,Z)=8

Q: A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white…

A: We have two random variables X and Y such that PYy=0 p0=121 p1=12 The conditional density…

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: Suppose that the number of accidents occurring on a highway each day is a Poisson random variable…

A: Givenλ=3.1 for each dayLet "x" be the no.of accidents occur in a dayx~Poisson(λ=3.1)P(X=x)=e-λ×λxx!…

Q: Let x1, X2, X3 be a random sample from an exponential distribution with mean 0. Consider the three…

A: The x follows exponential with mean is θ. Thus, the variance of X is θ2.

Q: A quiz is made up of 4 questions, where correct answers earn 1 point and incorrect answers earn zero…

Q: a) Let W = x1 + x2 be a random variable representing the total time to examine and repair the…

A: W = x1 + X2 i)The expected value is given by E(W) = E(X1) + E(X2) E(W) = 31.6 + 90 = 121.6 ii)The…

Q: Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the…

A: The correlation coefficient between two random variables X and Y is defined as: ρ(X, Y) = Cov(X, Y)…

Q: There are three random variables X, Y and Z, for which we know the following information E(X)= 6,…

A: Given: There are three random variables X, Y and Z. The given values are:…

Q: show all solution 1. Suppose X is a random variable with E(X2)=10 and E(X)=2. Find the following:…

A: Variance of constant is 0.

Q: Let X be a binomial random variable with parameters n = 20 and p ( p is intentionally not given in…

A: From the provided information, Sample size (n) = 20 Since the value of p is not provided therefore,…

Q: Suppose U = 2T - 1 where T is a geometric random variable with parameter p. What is Var(U)?

Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that P(4 < Y < 16) = P(A < X < B) μX=5σX=3μY=-2σY=6

Q: Given that X and Y are independent random variables and E(X) = 4, E(Y) - 7, Var(X) = 3. Var(Y) = 6.…

A: given data E(X) = 4, E(Y) - 7, Var(X) = 3. Var(Y) = 6. find Var(10X - 3Y) = ?

Q: Let X be a random variable from a Chi-Square Distribution with 13 degrees of freedom. Tatiana is…

A: We have to answer questions based on chi square distribution.

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: If Xn, n > 1, independent random variables and Xn 4 X (a random variable X), are

A: A degenerate distribution (sometimes called a constant distribution) is a distribution of a…

Q: 5) Let Y be binomial (n =4, II= .3) (a) Calculate the mean and variance by filling in the following…

A: A random variable X is said to follows binomial distribution with parameters n and p (i.e., B(n,…

Q: It's desired to model the random variable X with a shape that rises to a peak near x=6 and whose…

A: The PMF can be found by altering and standardizing the quantity shape.

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 be a binomial random variable with parameters of 9 and 0.1. Let Y be a binomial random…

A: Given that X+Y=2 So, the possible pairs are (0,2), (1,1), (2,0) So,…

Q: X is a discrete random variable such that the possible values are {a, a+1, a+2, ... b-1, b}. The…

Q: Let X and Y be independent random variables. Suppose X has variance 2 and let Y have variance 5.…

A: Given Data: Var(X)=2 Var(Y)=5

Q: A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white…

A: From the given information, fXx=∑yfX|Yx|ypYy, 0≤x≤100fX|Yx|0=31001-x1002fX|Yx|1=3100x1002PY0=PY1=12…

Question

100%

A random variable X~Binomial (2,1/3) is chosen, but the result is badly recorded; the record Y has an equal chance of being X, X+1, X+2.

a. Find the joint PMF of X and Y.

Y=0 Y=1 Y=2 Y=3 Y=4

X=0

X=1

X=2

b. Find the conditional PMF of X given Y

Y=0 Y=1 Y=2 Y=3 Y=4

X=0

X=1

X=2

c. The Y=2 column of your second table should match the marginal distribution of X (if it doesn't, check your answer). What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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: Finding the Joint Probability Mass Function of X and Y

VIEW

Step 2: Finding the Conditional PMF of X given Y

VIEW

Step 3: Usefulness of the value of Y=2 in guessing the value of X

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose the distribution of some random variable X is modeled as Negative binomial with parameters, p and r, where p is the probability of success and r is the total number of success over the trials. Find the method of moment (MM) estimators for (p,r), in closed algebraic form expressions based on a random sample of size n, X1, X2,...,Xn.
Let X,, X2, and X3 be independent random variables, each are binomially distributed with n = 100 and p = 0.2. Let A = X,– 2X2 and B = X3 + 3X1. Find PAB- %3D %3D
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
Suppose a random variable X has the following pdf. The random variable X has a Beta distribution with α = 3 and β = 2. Suppose we wanted to determine Var( 10X - 3 ). By the rules for variances, Var( 10X - 3 ) = * Var(X) + where, using the fact that X has a Beta distribution, Var(X) = Express answer as a decimal. Do not round.
A red die is rolled and then a green die. Let X=2(Spots on Red) + (Spots on Green). Determine the pmf for the random variable. In particular f(6)
16) number of medical tests that a patient will have on entering a hospital is a random variable X which can take on the values 0, 1, 2, 3, and 4. If P(X 2)=0.43, find P(X = 3).
Assume the flying height of an airplane is a Gaussian Random variable X with ax = 5000 m and ox=2000 m. Find the probability of the airplane flying higher than 10000 m. Use the table method.
Suppose that the time. in days, required to repair a heat pump is a random variable X having a gamma distribution with parameters k = 8 and A = 2. What is the probability that on the next service call (a) at most 3 day will be required to repair the heat pump? (b) at least 2 days will be required to repair the heat pump? %3D %3D
Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?
2. Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and y be random variables with means μx and μy, variances σ2x and σ2y, and population correlation coefficient ρ (the Greek letter rho). Let a and b be any constants and let w = ax + by for the following formula. μw = aμx + bμyσ2w = a2σ2x + b2σ2y + 2abσxσyρ In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression σxσyρ is called the covariance of x and y. If x and y are independent, then ρ = 0 and the formula for σ2w reduces to the appropriate formula for independent variables. In most real-world applications the population parameters are not known, so we use sample estimates with the understanding that our conclusions are also estimates.Do you have to be rich to invest in bonds and real estate? No, mutual…
Suppose that the number of customers entering a bank in one hour is a Poisson random variable and suppose that P(X=0)=0.02. Find the mean and variance of the variable. X: Number of customers entering a bank in one hour E(X)= Answer (Give the exact answer) V(X)= Answer (Give the exact answer) What is the probability that 5 customers will enter in two hours? Answer: Note: Answer with at least 4 decimal places
3.Suppose that X and Y are independent random variables for which Var(X)=Var(Y)=3. Find the values of (a) Var(X-Y); (b) Var(2X-3Y+1).