1. Suppose X1, X2, ..., X10,000 are independent random variables with E(X;) = 8 and Var(X;) = 4 for each i. Let Y = (X1+ X2 + ... + X10,000)/10,000. a. Find E(Y). o. Find Var(Y). c. What does the Chebyshev inequality say about P(|Y – E(Y)| > 0.1)? -

1. Suppose X1, X2, ..., X10,000 are independent random variables with E(X;) = 8 and Var(X;) = 4 for each i. Let Y = (X1+ X2 + ... + X10,000)/10,000. a. Find E(Y). o. Find Var(Y). c. What does the Chebyshev inequality say about P(|Y – E(Y)| > 0.1)? -

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: Suppose n> 1. Let X₁, X₂, mean and variance o². Let X₁ = (a) Var(4X₁-3X₂) DLX21 Xn be independently…

A: Let are iid with mean and variance .Let

Q: Consider a discrete random variable X with a pmf given by i) ii) iv) p(x) = cx2, if x = 1,2,3,4 0,…

Q: Consider that X₁, X₁...... X are random variables and the variance of each variable is 1 and the…

A: Given that V(X1)=V(X2)=...+V(Xn)=1 and r(Xi,Xj)=14i≠jWe have to calculate V[X1+X2+...+Xn]

Q: Let X, Y are random variables (r.v.) and a, b, c, d are values. Complete the formulas using the…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let X1, X2,... be independent Exponential (3) random variables and Z = } E=1 X;. If Mz (t) is the…

Q: Q.3. Let X be the random Variable with the following probability distribution: X: 9 P(X): 1/6 1/2…

A: Note: According to Bartleby, expert solve only one question and maximum 3 subpart of the first…

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Since, you have you have posted a question with multiple subparts we will solve first three subparts…

Q: 1. Decision Theory Consider the following random variable X. For positive integers k, Pr[X = 2k] =…

Q: Let N be the last digit of your student number. Let X and Y be two continuous random variables that…

A: Given data, Let N be the last digit of your student number. Let X and Y be two continuous random…

Q: 4. Let X be a discrete random variable with E (X) = 3 and Var(X) = 0.5, What are the mean and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let X₁, X2, X3, X4, X5 be an independent and identically random variables following a Binomial…

A: Dear student, According to Bartleby guidelines we can answer only first 3 subparts at once. If you…

Q: 3. let f(x) and F(x) denote respectively the p.d.f and the distribution function of the random…

A: f(x) and F(x) are pdf and cdf of the random variable X respectively.Conditional p.d.f of X is Where,…

Q: 2. Assume that the prices paid for housing within a neighborhood have a normal distribution, with…

A: We have given information, Assume that X be the prices paid for housing within a neighborhood have a…

Q: Let X be a r.v. with mean 4 and variance 5. Find an upper bound forP (X − 4 ≥ 8 ∪ X − 4 ≤ −8).…

A: Feel free to ask for further explanations!

Q: 2. If X, Y are independent random variables show that variance (X-Y)= variance (X) + variance (Y).…

Q: 2. A bucket has three marbles. Two are black and one is white. You keep drawing until you get a…

A: Given information A bucket has 3 marbles 2 Black, 1 white X denotes the total number of marbles…

Q: 3. If X is x² (23), find the following: a) P(14.85 < X < 32.01) b) constants a and b such that P(a <…

A: i.e. X follows chi-squared distribution with 23 degrees of freedom.

Q: 2. Prove Chebyshev's Inequality: Let X be a random variable with mean and variance o². Then for any…

A: First we define the variance definition Var(X)=E[(X-μ)2] expanding the above equation…

Q: The mean of a discrete random variable x. Select one: O a. is none of these b. is correctly…

A: The mean of a discrete random variable is customarily denoted by μ.

Q: The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours…

Q: 2.3. Let X and Y be random variables and let A be an event. Prove that the function Z(w) = is a…

A: We know that,A random variable is a numerical description of the outcome of statistical experiment.…

Q: 3.a. Fill in the blank and prove the resulting statement: If X is a random variable and t is a…

A: Result E(ax+b)=aE(x)+b V(ax+b)=a^2V(x) Given E(x)=7 , V(x)=2

Q: 24. Let X1, X2, .., X 100 be a random sample of size 100 from a distribution with density S(2) = {6…

A: Given that the pdf of random variable X is f(x)=e-λ*λxx! ; for x=0,1,2,......0…

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

Q: 2. A. let the p.m.f of X is: p(x) = ab* x = 0,1,2,... a+b=1 Find the median of X ? B. prove that the…

A: The p.m.f of The median of X needed to be determined and the probability-generating function of (-x)…

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

Q: Q2. Suppose X and Sare the sample mean and sample variance associated with a random sample of size n…

A: Given information Mean (µ) = 50 Standard deviation (σ) = 9 Sample size n = 16 Finding the Z- value…

Q: 0. Let X denote the number of hours you study during a randomly selected school day. The probability…

Q: If X, and X2 are the means of independent random sample of sizes n and n2 from a normal population…

A: Minimum varience of z=w*x1bar+(1-w)*x2bar is =sigma^2/(n-1+n2)

Q: Ex. 2. A random variable X is exponentially distributed with the deviance 1/4. Compute the…

Q: 3. V, W, X and Y are independent random variables, each having a normal distribution. V has mean 4…

Q: Let X and Y be independent random variables, both being equally likely to be any of the values 1, 2,…

A: The and are independent random variables. and takes equally likely to be any of the values .

Q: 5. The random variable X represents the number of cherries in a cherry puff, and has the probability…

A: Solution

Q: -. Determine the constant c so that f(x)=cx, x=1, 2, 3,...,10 satisfies the conditions of being a p.…

A: The given probability distribution can be desctibed as X 1 2 3 4 5 6 7 8 9 10 f(x) c 2c 3c 4c…

Q: 1. Let X1, X2, X3 be identically distributed independent exponential random variables and Y = X₁+ X2…

A: Given that X1, X2, and X3 are identically distributed independent exponential random variables…

Q: Suppose X1, X2 are i.i.d. random variables, each uniformly distributed on {−1, 0, 1}. Find the…

A: The i.i.d. random variables are and .Each follows a normal distribution on .The transformed…

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: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Given Information: Consider X, Y and Z are jointly distributed random variables. Consider the…

Q: Let X be a random variable having p.d.f. fx(x) = cx², -2 < x < 2. For the following parts, your…

A: Given density function: fx=cx2, -2<x<2 c value: ∫-22fxdx=1 from the total probability…

Q: Suppose we randomly draw two integers from the range [1, n] with uniform probability. Define X to be…

A: E(|X-Y|) fx|y=1n2 E(Z) = ∑x=1n∑y=1nx-yn=∑x=1n ∑y=1n x-yn2+∑…

Q: 3. Suppose X1 and X2 are independent random variables w. Let U = X1 and V = X1+X2. Find p(U, V) in…

A: Result X1 and X2 are independent, then Cov(X1, X2)=0

Q: 3. Let X and Y be i.i.d. standard normal random variables. Find E[X2 +Y²] and EVX² +Y².

Q: 2. A random sample X₁, X2, X3 of size 3 is drawn from a population with mean and variance o². Let 01…

Q: Let X1, X2,...,X3 denote a random sample from a population having mean u and variance o2. 302 Which…

Q: 4. Suppose that the random variable X has p.d.f. S1- |r – 1|, if 0 0.5. (c) Find the mean and…

A: for a pdf of random variable X, ∫-∞∞f(x)dx=1 . Pr(a<X≤b)=∫abf(x)dx. The mean and variance of X…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

4. Suppose X1, X2,..., X10,000 are independent random variables with E(X;) = 8 and
Var(X;) = 4 for each i. Let Y = (X1+ X2 + ... +X10,000)/10,000.
a. Find E(Y).
b. Find Var(Y).
c. What does the Chebyshev inequality say about P(|Y – E(Y)| 2 0.1)?

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

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

Let X1, X2, and X3 be uncorrelated RVs each with the same mean, µ, and variance, o?. Find expressions for the following in terms of the mean and variance: 1. Cov(X1 + X2, X, + X3). 2. Cov(X1 + X2, X – X2).
4. Sixteen-ounce boxes of shredded wheat cereal packed automatically by machine are sometimes over- weight and sometimes underweight. The actual weight in ounces over or under 16 is a random variable X whose probability density is f(x) = c(4- x²) for -2 < x < 2, and 0 elsewhere. Negative values pertain to ounces under 16. Determine the constant c, and then find the probability that a box of cereal will be (a) more than one ounce underweight.
1. Answer the following questions using the probability tree below: .2 .3 X .3 .8 a Y (a) What is the value of z? (b) What is the probability of X occurring? (c) What is Pr[Xa] (Note: Pr[Xa] = Pr[X and a].) (d) What is Pr[X_or a]? (e) What is Pr[a|X]? (f) What is Pr[c]?
show that if X11, X12,..., X1, X21, X22,..., X2n₂ are independent random variables, with the first n constitut- ing a random sample from an infinite population with the mean μ₁ and the variance of and the other n2 constitut- ing a random sample from an infinite population with the mean μ2 and the variance o2, then 1 M2 (a) E(X₁-X₂) = μ₁ −μ2; 07 0 22 (b) var(X₁-X₂) = + n₁ n₂
1.) The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours which is found to be uniformly distributed. Let x be the time needed to fix an A/C unit. b.) Find the probability that a randomly selected A/C unit repair requires less than 3.5 hours?
Suppose (S, P) is a binomial distribution with n trials and probability of success p. Let X be the random variable X(k) = k³, where k is the number of successes. Calculate E[X].
Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0
Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15
3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
X 1. A random variable is given by the table -2 1 3 4 P(X) | 0,2 | c | 0,3 | 0,1 Find constant c and then the mean value and variation.
Q.3. Compute the probability that: (a) their sum is odd; (b) their product is even. Three distinct integers are chosen at random from the first 15 positive integers.