Answered: et X denote a beroulli random variable,…

et X denote a beroulli random variable, that is P(X=1) =p and P(X=0)=1-p and let Y be a binomial random variable with parameters n and p. Show that X+Y is binomial with parameters n+1 and p

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: how to find E(X), E(Y), E(X^2)

A: Given that X and Y are independent and follows N(0,1)

Q: Suppose that two random variables Y1 and Y2 are independent, that is, for all values of Yı and y2,…

Q: Suppose X is a random variable such that EX = 50 and V arX = 12. Find (a) E(X 2 ) (b) E(3X + 2) (c)…

A: The given X is a random variable with EX=50 and VarX=12.

Q: Just a regular student: Alex, your friend and a hard-working student with anxiety is enrolled in a…

A: Given that, X~ Uniform (3.5, 5) There are total 12 quizzes in a course (X1, X2,...,X12) Q. a) The…

Q: Customers arrive at a service facility according to a Poisson process of rate A = 3 per hour. Given…

A: Customers arrive at a service facility according to a Poisson process of rate .

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

Q: S Suppose that the time (in hours) required to repair a machine is an exponentially distributed…

A: The distribution of the repairing time for the machine is specified to be distributed exponentially…

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: IF X is a binomial random variable in a binomial experiment with p=3/4 and n=4 find(X=2)

A: Binomial Distribution: Suppose we have n trials each having two outcomes, say Success and Failure,…

Q: If x is a binomial random variable, compute P(x) for each of the following cases: (a) P(x\leq 6)…

A: If X~Bin(n,p) P(X=x)=nCxpx(1-p)n-x x=0,1,2,..,n Farmula used nCr=n!/(r!(n-r)!)…

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

Q: Let X(n,p) denote a binomial random variable with parameters n and p. Show that X(n+1,p)>=st X(n,p).

A: Given To prove that

Q: Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either…

A: We know, In probability distribution, the weighted average of possible values of a random variable…

Q: Show that if a random variable has a uniform den-sity with the parameters α and β, the probability…

Q: For a uniform random variable U∼U(2,11)U∼U(2,11), find the probability P(U<9)P(U<9): P(U<9)=P(U<9)=…

A: GivenA random variable x~Uniform(2,11)f(x)=1b-a ; a<x<bf(x)=111-2f(x)=19 ;…

Q: Suppose that X and Y are independent normal random variables and - XE N(6,1) Y € N(8, 2) Find P(X -…

A: We have given that , X€N(6,1) Y€(8,2) . We have to find, P(X-Y>0) = ?

Q: The number of times that a person has a cold each year is a Poisson random variable with parameter λ…

A: Define the event E as the drug works, thus P(E)= 0.75 The drug that doesn't work is the complement…

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: The Mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. Find A and B, both greater…

A: Given that X follows Normal(mean=5, SD=3) Then Z=(X-mean)/SD= (X-5)/3 follows standard normal…

Q: Let X1 and X2 be independent random variables with respective binomial distributions b(3,1/2) and…

A: The provided information is as follows:The and are two independent variables.The follows binomial…

Q: d) What is the standard deviation of T? e) What is the probability that T is within 2.0 standard…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: Prove that the mean and variance of a binomially distributed random variable are respectively: mu…

A: Expected value:The expected value is given below:

Q: If X∼U(4,18) is a continuous uniform random variable, what is P(12<X<16)?

Q: Let x be a binomial random variable with n = 20 and p = 28 / 100 Find P (2 ≤ x ≤ 4) and P (x > 1).

A: Given: n=20 p=0.28

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

A: Given X is a binomial random variable Number of trials=n=167 Probability of success=p=0.051

Q: If X and Y are two independent random variables, then Ox+y(@) = x (@) 0, (@) %3D

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

A: Given X is a binomial random variable n=No. of trials=125 p=Probability of success=0.016

Q: If the random variable X is binomially distributed with p-0.75 and o-0.7125, then P(X=1) is

A: The provided information are: Meanμ=0.75Varianceσ2=0.7125

Q: If x" bin(n1,p) and x2~bin(n2,p) then find the distribution of x1|x1+x2 ; where x1 and x2 are…

Q: Where does the z=2 come from? Just from X, and Y also being random variables?

A: Solution of the asked question is in step below.

Q: Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X − Y) = 2,…

A: SOLUTION: Cov(X,Y)=np(1-p)-1

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: Let n be a random sample from the exp(0) Show that X is a sufficient statistic for

A: Given X~exp(θ)

Q: let X(n,p) denotes binomial random variable with parameters n and p. Show that X(n+1,p) >st (…

A: Given Information: X(n, p) denotes binomial random variable with parameters n and p where n is the…

Q: Suppose X and Y are independent random variables with X - B (n, p) and Y ~ B (m, p). Show that X +Y…

Q: A scheme of random number generator is described as follows. First, one generates a normal random…

Q: Q1:Show that: If X1, X2, ., X, are independent random variables and X = X1 + X2 +….+ X, , then Q2:…

A: Note: As per bartleby guidelines for more than one questions asked, only one question is to be…

Q: Let X denote the number of bits received in error in a digital communication channel, and If 100 bit

A: We have to find given probability...

Question

let X denote a beroulli random variable, that is P(X=1) =p and P(X=0)=1-p and let Y be a binomial random variable with parameters n and p. Show that X+Y is binomial with parameters n+1 and p

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

SEE SOLUTION Check out a sample Q&A here

Similar questions

20
If the discrete random variable X takes on the values 1 , 2 , 3 and if P ( X = 1 ) = P ( X = 3 ) = 0.2 then the mean of x =
For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true False
Let Z be a random variable with E(Z) = 12 and Var(Z) = 5. Based on the statement above, determine which of the following statements are true and false. Show complete solution. a) E(3Z + 10) = 46 b) E(Z^2) = 160 c) Var(10)=10
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)
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 X is a random variable * ? having the following m.g.f., Find Var(x) 7t_e4t M, (t) = eT 173 O 5 O 413 O 3148 O 55 O
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).
Let x1, x2, .. xn be independent standard normal random variables, where n = 9. What is the probability that 3 of them have values in the range [1, 2]? This is how alpha is computed for some sentizing rules. Use 7 decimal places.