A routine question from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for self-study questions.

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5 views

Expected lifetime of a device with two parts each having spares?

Consider a device with two parts : (1) and (2). Part (1) has 2 spares and part (2) has one spare. Lifetime of part (1) and its spares have iid exponential distribution with rate lambda. Lifetime of ...
2
votes
1answer
32 views

Given a chi-squared distribution, find $\Pr(Y \in \mu \pm 2\sigma)$

Given a chi-squared distribution of df = 8, which R command do I use in order to find $P(Y \in [\mu \pm 2\sigma])$? That is, the probability that $Y$ lies within 2 standard deviations of its mean? I ...
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0answers
13 views

Help finding critical on a hypothesis contrast

I´ve tried finding the variance using the moment-generating function but apparently that is not the correct method for finding the critical. Can you help me with this?
0
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0answers
21 views

Maximum Liklehood estimator of Poisson

I am trying to solve the following problem, I was able to solve first three bits of the problem but after that i am stuck and do not have clue to solve the (iv) bit. The local government has ...
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0answers
22 views

How to solve hat check problem using R? [on hold]

Suppose n people go to a fancy restaurant. Each person is wearing a hat and checks his/her hat at the door as he/she arrives. The hat-check attendant gets tipsy throughout the evening, forgetting ...
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3answers
53 views

For Y~B(11, 0.3) what is P(|Y-5| >= 3)?

I feel this is a simple problem, yet I cannot seem to solve it. Any help is greatly appreciated.
1
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1answer
43 views

bivariate normal density function

I know how to show the first part, but I am confused about the second part, how to express the relationship between the two? Any hint, advice or suggestion is appreciated.
2
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0answers
24 views

How to determine a probability that 100% of confidence intervals from a bootstrap contain the true mean

Say I take 500 bootstraps of a population and calculate 95% confidence intervals (CIs) for each sample. I would expect that 95% of the bootstrap sample CIs to contain the true population mean. ...
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0answers
15 views

Probability of occurance of events in time-window [on hold]

Question: After locking the car, what is the probability that car may be unlocked within X seconds? If X is 1 seconds, then I guess probability is very low. If X is say 60 seconds, then probability ...
1
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1answer
87 views

Mutual Exclusivity

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. A. List sample ...
1
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0answers
59 views

Normal Distribution with mean and standard deviation

I'm trying to solve the following problem: Suppose at breast height, the diameter of trees of a particular type is normally distributed with mean=8.8 inches and standard deviation= 2.8 inches.What ...
1
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1answer
106 views

Finding the sample space of an experiment

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. List the sample ...
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0answers
24 views

Probability question- From Mathematica program

Could somebody please help me, I have been trying to calculate this problem all day, but with no success. Here is the problem: "A teacher was asked by her principal to select 7 students at random ...
2
votes
1answer
34 views

Calculating the expected value and variance of an estimator of a normal quantile

I don't quite understand how to use the estimator function and the variance function and plug in the sample mean. I expected that we would plug in the value $\bar X - 1.645s$ into $E(s)$ and $V(s)$. ...
4
votes
2answers
72 views

Problem obtaining a marginal from the joint distribution

Suppose $X_1$ and $X_2$ have the joint pdf $$f_{X_1,X_2}\left(x_1,x_2 \right)=4x_1 x_2,\quad\text{for}\quad 0<x_1<1, 0<x_2<1$$ From that I found the joint pdf of $Y_1=\frac{X_1}{X_2}$ ...
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2answers
44 views

Different results from several “passes” of Random Forest on same dataset

I've been playing around with the German Credit dataset available in Kuhn & Johnson's caret package for ...
1
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2answers
23 views

Need help finding the probability

I have problem where you are given the number of times you must win, and the chance of winning a game. I need to find the probability that I win all 4 times. Example: I am only given two inputs, 4 ...
0
votes
0answers
38 views

Bayesian Data Analysis, 3rd edition: Problem 8.8

I'm self studying with the 3rd edition of Bayesian Data Analysis by Gelman et. al. Currently reading through Chapter 8 and trying out some of the problems. Question 8.8 has me baffled on how to solve ...
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0answers
20 views

Error in gnls step halving factor

I am getting an error running a gnls() on some data I have. I was able to converge using nlsLM(), but I ran into some autocorrelation in my errors, so I want to try to use gnls() so that I will be ...
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0answers
7 views

On the derivation of the closed form Yule-Walker moment estimator of a GARCH(1,1). (exercise)

The exercise states: (Yule-Walker estimator) GARCH models are typically estimated by a numerical implementation of maximum likelihood methods. This procedure has the disadvantage that it does ...
2
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1answer
39 views

On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations

For an AR(2) I can get the Yule-Walker equations: $$\begin{cases} \rho_1=\alpha_1+\alpha_2\rho_1 \\ \rho_2=\alpha_1\rho_1+\alpha_2 \\ \rho_k=\alpha_1\rho_{k-1}+\alpha_2\rho_{k-2} \end{cases}$$ ...
2
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1answer
44 views

Proving for an AR(2) process that $E[X_t | F_{t-1}]=E[X_t | F_{t-2}]=E[X_t | F_{t-3}]$

An exercise states: Using the law of iterated expectations applied to an AR(2) process, verify that $E_{t−k} . . . E_{t−1} (X_t ) = E(X_t |F_{t−k} ) $ for $ k = 1, 2, 3 $ where $ E_{t−k} (X_t ) = ...
1
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1answer
30 views

Comparing Variability

Question: Constant velocity joints (CV joints) allow a rotating shaft to transmit power through a variable angle, at constant rotational speed, without an appreciable increase in friction or play. An ...
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0answers
15 views

Comparing 2 Likert Scale's data with different sample size

I have asked questions on a 5 point Likert scale (1=strongly disagree, 5=strongly agree), and I want to do two types of comparisons: Compare responses of non-users vs. users in country A. Compare ...
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2answers
119 views

Characteristic function problem

Suppose $X_1$ and $X_2$ are independent random variables and suppose also that $X_1$ and $X_1-X_2$ are independent. Show that $$\mathbb{P}_{X_1}[X_1=c]=1$$ for some constant $c$. What I get so ...
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1answer
64 views

Tossing 2 coins, distribution

We are tossing 2 fair coins once. Then for the next toss we are only tossing the coin(s) that came up heads before. Let $X$ be the total number of heads. The question is $EX$ and the distribution ...
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1answer
29 views

Correlation of linear combination of random variables [duplicate]

How do I proceed further? (assuming what I did is correct in the first place)
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0answers
24 views

Find the distribution of the supremum of the Brownian motion

Let $A(t)$, $t \in [0,1]$ be a Gaussian process with zero mean and co-variance kernel $\mathrm{Cov}(A(t_1),A(t_2))= \min (t_1,t_2),\, \forall t_1,t_2 \in [0,1]$. Find $$P\left[\sup_{t \in ...
2
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1answer
63 views

What would be the likelihood function of a pdf, $p(n)=1-|n|$ for $|n|<1$?

This might seem like a basic question to some but I am utterly confused by the fact that the given pdfs are not Gaussian or any other distribution commonly seen in examples. I have two hypotheses ...
2
votes
2answers
51 views

Question on the correlation between two dependent variables

I'm working on this question and it's stumping me. Let $S_n = X_1 + \ldots + X_n$ (with $n>=1$) be a random walk with $X_1, \ldots, X_n$ be iid RV's. $$ E(X_k)=\mu,\,{\rm Var}(X_k)=\sigma^2. ...
2
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1answer
64 views

Question about MGF

I got multiply two taylor expansions, however, I do not know how to differential it by r times respect to t in this multiply of two taylor expansions.
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0answers
27 views

Standard Deviation and Variance

Can someone help me with this question because I'm not sure of how to do it exactly: There are two routes for a worker to get to his office. Both the routes involve hold ups due to traffic ...
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0answers
70 views

Badidas and Nikit Shoes

Good day everyone, I am self studying statistics at home and in the office whenever i have time. I want to improve my reporting. So i just came across this website and decided to try if could ask a ...
0
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1answer
41 views

statistical hypotheses

A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.With a significance level of 1%, can ...
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1answer
28 views

Most probable value given observation

Suppose I have observed $Z = 3$, where $Z = X + Y$, where $X \sim N(0,9), Y \sim N(0,4)$. How would I find the most probable value of $X$ that would have given me $Z = 3$? My attempt at a solution: ...
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1answer
20 views

Relationship between nominal and ranked variables

I am practicing statistics on the gss dataset. I want to study the relationship between people owning guns in the USA and political inclination. Owning guns or not is a nominal variable while ...
1
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1answer
24 views

What is the statistical power of a test when the true population mean is unspecified?

I have been given the following homework problem: To improve the reading scores of its students, a school district randomly selects 50 students to participate in a new program. The mean reading ...
0
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0answers
36 views

Probability distribution of time series

I am unable to understand concepts related to the probability distribution of binary time series. This is from the book Binary time series by Benjamin Kedem, vol 52 Let $X_t$, t =0,1,... be a binary ...
2
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2answers
61 views

Jointly sufficient statistic?

A random sample $X_{1},...,X_{n}$ is pulled from a gamma distribution. Are there jointly sufficient statistics based on these observations for the two unknown parameters? The definition of a gamma ...
3
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0answers
17 views

Logistic regression variance [duplicate]

So far I have checked the tolerance value, VIF and condition indexes. But checking the variance of the regression coefficients I have to wonder: how little variance of the regression coefficient ...
0
votes
2answers
58 views

Maximum Likelihood estimator from sample distribution $N(0,\sigma^2x_i^2)$

Let independent random variable $Y_1,...,Y_n$ have respective distributions $N(0,\sigma^2x_i^2)$, where $i=1,2,...,n$ are known constants such that $x_i\neq 0$ for all $i=1,2,...,n$. Find the maximum ...
2
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0answers
34 views

Finding $Var(S^2), E(S^4),$ and unbiased estimator for $\sigma^4$ from random, normal samp

Let $X_1,...,X_n$ be a random sample of size $n$ from the normal distribution $N(\mu,\sigma^2)$ and let $S^2$ be the sample variance. (a) Find $V(S^2)$ and derive $E(S^4)$. (b) find an unbiased ...
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2answers
48 views

$Var(\bar{X})$ for a random sample from Bernoulli Distribution

Let $X_1,...,X_n$ be a random sample of size $n$ from a Bernoulli distribution with parameter $p$ where $0< p< 1$ is unkown. (a) Find $\theta^2=Var(\bar{X}).$ (b) Find the value of $c$ so that ...
0
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0answers
17 views

Loss Elimination Ratio

The values in Table 8.2 are available for a random variable X. There is a deductible of 15,000 per loss and no policy limit. Determine the expected cost per payment using X and then assuming 50% ...
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0answers
21 views

Sample size for a Pilot study [closed]

What will be the sample size for a pilot study?
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0answers
61 views

Ap Stats Need Help on Assessing Normality

Grey Kangaroos are large, social marsupials, indigenous to Australia. The Eastern Greys are a light grayish brown, while the Western Grey is a copper brown color. As part of a study of the ...
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0answers
12 views

sensitivity and specificity over different strata

I'm curious if there's a standard way to compute a sensitivity/specificity score if I collect over different strata. Obviously, I can calculate it per stratum and then weight it using the proportion ...
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1answer
48 views

Constrained MLE of multivariate normal

this might be obvious one but I have spent much time without gaining anything. If $\underline{X}$~$N_p(\underline{\mu},\sigma^2 I)$, where $\mu$ is known to lie on the unit sphere ($\mu^T\mu$), show ...
4
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0answers
42 views

A proof for the stationarity of an AR(2)

Consider a mean-centred AR(2) process $$X_t=\phi_1X_{t-1}+\phi_2X_{t-2}+\epsilon_t$$ where $\epsilon_t$ is the standard white noise process. Just for sake of simplicity let me call $\phi_1=b$ and ...
2
votes
1answer
64 views

Identifying the coefficients of a principal component

Suppose that a two-dimensional random variable $X$ has a covariance matrix given by $$ \Sigma = \pmatrix {1 & -2\\ -2 & 4}$$ One of the three linear combinations below corresponds ...