# Tagged Questions

59 views

### Is there an alternative representation for $E[\max\{X,Y\}]$?

Suppose we have $X,Y$ i.i.d. Is there a simplified form of $E[\max\{X,Y\}]$? Is it just $\max\{E[X],E[Y]\}$? That doesn't seem right, because the latter would just be $E[X]$, and it seems like taking ...
141 views

### 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 $E(X)\le \sum_{n=0}^{\infty}P(X>n)$.
108 views

### Expected number of cards drawn

You draw cards from a standard 52-card deck without replacement until you get a queen of spades and stop. The cards have the values $2,3,4,\ldots,11(J),12(Q),13(K),14(A)$. The first card you draw ...
67 views

### 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 ...
109 views

### 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 ...
66 views

127 views

### How to express the expected value of revenue w/ reserve price in 2nd price auction?

Breifly speaking, the problem comes from setting a reserve price in 2nd price auction, where w/o a reserve price $a_t$, the winner pays the 2nd highest bid $b_t$. But w/ a reserve price, the winner ...
61 views

207 views

### Meaning of this expectation equation?

I was actually looking at this problem on slide 12. I will write it here briefly: Problem: Unknown number of people arriving in a fixed time period and my goal is to maximize my probability of ...
This is in reference to the Girsanov theorem however question is general. If $X$ is a standard normal variable $N(0,1)$, why is expectation of $e^{-\mu X - \mu^2/2}$ equal to 1? Shouldn't it be ...