# Tagged Questions

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### Show that if $X\ge 0$ , $E(X)\le \sum_{n=0}^{\infty}P(X>n)$

If $X$ is a random variable and also let $X\ge 0$. I want to show $E(X)\le \sum_{n=0}^{\infty}P(X>n)$.
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### Is E(u|x)=0 is a required condition for estimator consistency?

For OLS parameter estimates to be consistent it must be the case that E(u|x)=0. Is it true? E(u|x)=0 is a required condition for unbiasedness. But as far as I understand, unbiasedness does not ...
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### How to prove three properties of the moment generating function? [duplicate]

The moment generating function of a random variable $X$ is defined to be the function $$M_{X}(t)=E(e^{tX})=\sum_{n=0}^{\infty}\frac{E(X^n)}{n!}t^n.$$ Let $I=\{t\in\mathbb R:M_{X}(t)<\infty\}.$ I ...
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### I want to show $E(X)=\sum_{n=1}^{\infty}P(X\ge n)$

Let $X:\Omega \to \mathbb N$ be a random variable on probability space $(\Omega,\mathcal B,P)$ .show that $$E(X)=\sum_{n=1}^{\infty}P(X\ge n).$$ my definition from $E(X)$ is equal ...
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### Demand with different Measurement

Weekly's demand of a product has a probability function ...
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### How would I calculate the expected change?

Based on the info below, how would I calculate the expected change in the test scores for males and females? The company decides to test for differences in performance across genders. To do so, they ...
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### Taking the expectation of Taylor series (especially the remainder)

My question concerns trying to justify a widely-used method, namely taking the expected value of Taylor Series. Assume we have a random variable $X$ with positive mean $\mu$ and variance $\sigma^2$. ...
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### Probability Questions

I've got a 2 advanced probability questions that I'm having trouble with so just asking to confirm an answer/method A computer company provides an insurance policy for one of its systems. If the ...
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### Need clarification: averaging over the training set for an estimation?

I am reading Elements of Statistical Learning and this is a passage in chapter 2: This Expected Prediction Error was clear for me previously: there is an unknown ground truth mapping between the ...
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### Joint distributions for uncorrelated varibles

Can someone think of joint distribution of random variables X, Y such that the following three conditions are satisfied: $E[X] = 1$, $E[Y] = 1$, and $E[XY] = 0$? A friend of mine asked me this, ...
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### the expected value of your gain

You flip a coin and if it is a head I pay you 1 pound but if it is a tail you pay me 2 pounds. You have 50 pounds and you stop when you spend all of your money or you flipped coin 100 times. What is ...
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### Given a table defining the joint probabilities, how do I calculate certain parameters of the marginal distributions?

The number of items sold on any one day in the traditional shop is a random variable X and the corresponding number of items sold via the Internet is a random variable Y. The joint distribution of X ...
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### How to find Coefficient of Variation with E(X), E(X^2) and sample size?

Given E(X), E(X^2) and sample size. How do I find Coefficient of Variation? Variance = E(X^2) - E(X)^2 sd = square root of variance Coefficient of Variation = sd / E(X) however, with the values ...
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### Finding correlation coefficient

if I have A and B with the following known variables: with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$ and correlation coefficient: $\rho_{AB}$ (assign numbers if you like) Say: $C=0.6A+0.4B$ Then ...
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### Expected value (Chi-Squared) [duplicate]

Possible Duplicate: Why is sample standard deviation a biased estimator of $\sigma$? Let $X_1, X_2, X_3 \sim N(0, d^2)$ and $T = X_1^2 + X_2^2 + X_3^2.$ T is chi-squared distributed, ...
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### Conditional Expectation / Estimator Confusion

Let $X_1, X_2, X_3 \sim N(0, d^2)$ and $T = X_1^2 + X_2^2 + X_3^2.$ I have an estimator for $d$, $$\hat{d} = \frac{\sqrt{T\ 2\pi}}{4},$$ and another estimator for $d$, \tilde{d} = \frac{1}{3} ...
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### Sum of Gamma distributions

The lifetime of a particular brand of batteries is known to have a gamma distribution. Tests on a large sample of these batteries show a mean lifetime of 480 hours and a standard deviation of 96 ...
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### Show that Y/Z does not have finite expectation

The unit interval (0, 1) is divided into two sub-intervals by picking a point at random from inside the interval. Denoting by Y and Z the lengths of the longer and the shorter sub-intervals ...
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### Find probability and expectation

18 boys and 2 girls are made to stand in a line in a random order.Let $X$ be the number of boys standing in between the girls .Find $P[X=5]$ and $E[X]$. I proceed in this way: Note that ...
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### Expected number of failures preceding the first success

I am a beginner in statistics and probability. I have a question that says What is the expected number of failures preceding the first success in an infinite series of independent trials with the ...
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### Determining the expected number of accident-free days per year in a city

If a city has an average of two accidents per day, how many accident-free days do you expect in a year?
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### How to calculate expected value and standard deviation if I have 100 values divided into 15 groups (normal distribution)?

These are the values: ...