Answered: Assume X and Y are independent random…

Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)

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: f x is a binomial random variable, find p (x) for n = 6, x = 3, p = 0.5.

A: Solution: Let X has binomial random variable with parameter n= 6 and p= 0.3 X~B(n=6,p=0.5) The…

Q: Show that adding a constant K to a random variable increases the average by K but does not change…

A: Suppose I have a below data For random variable X 2,5,8,4 consider k= 2 Average of 2,5,8,4 using…

Q: Q16. Ris a Binomially distributed Random Variable such that r~ B(10,0.4). Which of these statements…

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

Q: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

Q: An electrical firm manufactures light bulbs that have a length life with normal distribution, and…

A: Since the population of the life time of the light bulbs being sampled from following a normal…

Q: Suppose X is a binomial random variable with parameters n=18 and p=0.5 Calculate the mean and…

A: For the given question- Mean: 9 Variance: 4.5Explanation:Solution- To calculate the mean and…

Q: True or false: P(X-7)=P(Y=3).

A: Let X be a binomial random variable with n=10 and p=0.3. Let Y be a binomial random variable with…

Q: For a binomial random variable X, n = 15 and p= 0.60. Find P(x= 5)

A: Answer: From the given data, sample size (n) = 15 p = 0.60 X~ Binomial distribution (n,p)

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: Bob plays a game in which a dice is rolled until an odd number occurs. Bob wins 10 – x dollars if x…

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

Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

Q: Let X and Y and Z are uncorrelated random variables with the same variance. Find the correlation…

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: A binomial random variable X reveals p=100 and o=20. Calculate P{X=101}.

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: Suppose X is a normal random variable, and E(X) = 2. Find the probability that X will be within 2…

A: Suppose X is a normal random variable, and E(X) = 2.

Q: Suppose X is a binomial random variable with parameters n=10 and p=0.3 Calculate the mean and…

A: The mean of X is 3. The variance of X is 2.1. Explanation:Step 1: If X follows binomial…

Q: 3. Find the variance and standard deviation of the probability distribution of a random variable X…

A: Variance=EX2-E2(X)=22920+42120+5215+32310-2920+4120+515+33102=10.3-32=1.3

Q: Suppose that X is a N(3,4) random variable and suppose that Y=2X+1. Determine P(Y>8).

A: Given that X follows Normal distribution with mean =3 and variance=4 And Y=2X+1

Question

Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)

Video Video

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: find the expected value and variance

VIEW

Step 2: E(3X+2Y+1):

VIEW

Step 3: Var(3X+2Y+1):

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose that X1, X2, X3 and X4 are all independent random variables, each with a normal distribution with mean 9 and variance 25. Define X-bar = (X1 + X2 + X3 + X4) / 4. Find Prob(X-bar > 10).
Suppose two discrete random variables X and Y follows a Binomial distribution. If the random variable X follows Binomial with, X ~ bin (20, 0.25) and the random variable Y follows the Binomial with, Y~ bin(10, 0.35). 2. 3. i. ii. iii. Compute the expected value for X and Y. Compute the variance and the coefficient of variation for X and Y. Suppose further that there exist a random variable W, related to the random variables X and Y by the linear relation, W= 0.4X + 0.6Y and the Covariance( X,Y) is -0.0045, find the expected value of W, (E(W) ) , and the coefficient of variation of W. ( Hint use the transformation properties).
Previous Probletn Let X and Y be independent random variables. Suppose X has variance 2 and let Y have variance 5. Find Var(3X-2Y + 3). Please answer to 2 decimal places.
Assume that X₁, X2,..., Xn are independent and identically distributed random variables with expectation and finite variance o2. What is the approximate distribution of Sn = X₁ + X₂ + + Xn? (State all parameters of the distribution.)
Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).
Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175
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.
Prob and stat
A random variable X has mean 3 and variance 2. Use Chebyshev’s inequality to obtain an upper bound for P( |X -3| > 2). (answer must be in fraction)
The random variable Z has mean 30 and variance 225. Calculate the limits between which you would expect the bulk of observations to lie for the random variable Z/3 − 7.
Suppose that X is a N(3,4) random variable and suppose that Y=5X+2. Determine P(Y>18.5).
Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO