3k views

### Inverse transform sampling - CDF is not invertible

Suppose the cumulative distribution function $F$ is given but not invertible to use the inverse transform sampling technique (to compute $X=F^{-1}(Y)$). Do we have other alternative methods? I would ...
• 307
578 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 $E(X)\le \sum_{n=0}^{\infty}P(X>n)$.
• 403
10k views

### Expectation when cumulative distribution function is given

This is from the book Fundamentals of Probability with Stochastic Processes by Saeed Ghahramani, pages 249-250 which asserts, for any random variable $X$ that is non-negative, expectation of $X$ is ...
• 183
3k views

### What should the integral of a CDF be called?

This is strictly a nomenclature question. I have no particular problem finding double integrals of the type $\int\int\text{pdf}(y) \, d y \,d x$, and I find them quite useful. Whereas we have a good ...
• 12.5k
5k views

### Calculating life time expectancy

How to calculate life time expectancy when not all patients have died. Kaplan-Meier provides a survival curve which is similar to cumulative distribution function but not the actual expectancy. For ...
• 123
178 views

### Test two groups with only sample statistics or without distributional assumptions

I have two sets of samples, A and B. I want to find whether the underlying mean (i.e. if the sample size was infinite) of A is greater than that of B, to a certain confidence (95%). There are two ...
• 6,749
258 views

• 18.3k
176 views

• 33
1 vote