Let X1, X2, ... be a sample from a population that is geometrically distributed with p = }. (a) Use a suitable version of the Central Limit Theorem to estimate the probability 800 PEx; > 2450 (b) The negative binomial random variable was defined as a sum of a sample of geometric random variables. Why might this approach be preferable to just using the negative binomial PMF?

Let X1, X2, ... be a sample from a population that is geometrically distributed with p = }. (a) Use a suitable version of the Central Limit Theorem to estimate the probability 800 PEx; > 2450 (b) The negative binomial random variable was defined as a sum of a sample of geometric random variables. Why might this approach be preferable to just using the negative binomial PMF?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Let x be a binomial random variable with n = 20 and p = 0.2 Find p (x<5)

A: Given information: X is a binomial random variable. The parameters are: Number of trials, n = 20…

Q: ) John works at a phone bank. After getting off the phone with a particularly rude customer, he…

Q: The number of cakes baked on any business day in this bakery is a random variable that follows a…

A: The number of cakes baked on any business day in this bakery is a random variable that follows a…

Q: Under what conditions can the Poisson random variable be used to approximate a probability…

A: According to the given information in this questionWe need to identify the correct option

Q: Suppose a simple random sample of size n=1000 is obtained from a population whose size is…

Q: When a new drug is created, the pharmaceutical company must subject it to testing before receiving…

A: Given: Null Hypothesis: The Drug is unsafe Type 1 Error: Type 1 error occurs when we reject the…

Q: Find the following probabilities for the given random variables: a) X Normal(8, 16); P(X> 11.5) b) X…

A: a) X~Normal(8,16) Mean(μ)=8 Variance(σ2)=16 standard deviation(σ)=16=4

Q: Suppose 'W' is the width of all toilet seat covers used by all hotels in Paris. Suppose 'W' is…

A: n=36, mean μ=15 and the variance σ2=9 so the standard deviation is σ=3 Since the sample size is more…

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: The proportion of individuals that regularly smoke in a population is known to be 0.25. Applying…

A: Given that: p = 0.25 n = 1000

Q: An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular…

A: It is given that n =5,000 and p = 0.0005 (=1/2,000).The probability mass function of binomial…

Q: The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"†…

A: Let x = distance of actual landfall from predicted landfall. Suppose that the random variable x…

Q: Suppose X denotes the normal random variable with mean 5 and variance 4. Compute the following (a) P…

A: We have given that, X be the random variable from normal distribution with mean (μ) = 5 and…

Q: The mean number of breakdowns of a conveyor belt per month at a local factory is 56. Assume that…

A: Given : (i)Average rate of breakdown of the conveyer belt is 56 per month(ii)Breakdowns are random…

Q: Suppose a simple random sample of size n=1000 is obtained from a population whose size is…

A: Here is given that, sample is 1000 and proportion is 0.58. We will use binomial distribution to find…

Q: ose that we know, in addition, thất the standard deviation of the student's test on the final is…

A: We have given that. X~N( μ , ?^2 ) μ = 71.5 , ? =8.8 Z-score =( x - μ )/?

Q: If X is a binomial random variable, compute the probabilities below: (a) X - Binom(8,0.4) P(X 3)…

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

Q: If X is a binomial random variable, compute the probabilities below: (a) X - Binom(8, 0.4) P(X 3) =…

A: The random variable X follows binomial distribution. We have to find the probability by using pmf of…

Q: If we perform a paired t test and retain the null hypothesis, then what does this mean if we made…

A: The null and alternative hypothesis is,

Q: Consider a population of five units which are {1, 3, 4, 5, 5} (a) What is µ, the population…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute.…

A: Hi there! Thank you for posting the question. As there are multiple sub parts, according to our…

Q: A researcher wanted to test the mean of the binomial distribution as H0 : λ = 2 vs H1 : λ = 1. He…

A: To solve this problem, we need to use the binomial distribution formula and the significance level…

Q: Suppose that the population mean flight time between cities 1 and 2 is 240 minutes with a population…

A: Given that. X~N( μ , ?^2 ) μ=240 , ?=20 Z-score =( x - μ )/?

Q: A medical clinic opens at 9:00 am and then patients arrive according to a Poisson process with rate…

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

100%

**Geometric Distribution and the Central Limit Theorem**

Let $ X_1, X_2, \ldots $ be a sample from a population that is geometrically distributed with $ p = \frac{1}{4} $.

**(a)** Use a suitable version of the Central Limit Theorem to estimate the probability

\[
P\left(\sum_{i=1}^{800} X_i \geq 2450\right).
\]

**(b)** The negative binomial random variable was defined as a sum of a sample of geometric random variables. Why might this approach be preferable to just using the negative binomial PMF?

This problem explores the use of the Central Limit Theorem (CLT) for approximating probabilities involving sums of geometric random variables and discusses the benefits of defining a negative binomial random variable in this manner.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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, statistics and related others by exploring similar questions and additional content below.

Similar questions

According to a study, 50% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a dorm are counted as living at home). Suupose that a survey is administered and 121 of 209 respondents indicated that they live at home. (a) Use the normal approximation to binomial to approximate the probability that at least 121 respondensts live at home. (b) Do the results from part (a) contradict the study? Thanks!
A fair standard die is rolled 50 times. Let W be a random variable with binomial distribution thát represents the number of times the face with a six on it appears uppermost. Pr(W = k+1) _ (50 – k) 5(k +1) b. Show that %3D Pr(W = k)
Obtain the expected value of a random variable with four values 1,2,3,4 with probabilities P(1)= 1/4 ; P(2)=1/4 ; P(3)=1/8 ; P(4)=3/8
For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true False
Suppose that Y Binomial(n, p) (that is, discrete random variable Y has a Binomial distribution with parameters n and p, where n is a (strictly) positive integer, and 0 < p< 1).