# Tagged Questions

30 views

### Probability that the call will be answered at time $t$ is given by $f(t)$. Find the median waiting time for the call.

$$f(t) = \begin{cases} 0 & \text{if t < 0 } \\ 0.2e^{-t/5} & \text{if t\geq 0} \end{cases}$$.  Find the median waiting time for the call.  I cannot understand ...
22 views

345 views

### Computing an integral involving standard normal pdf and cdf - with peculiar limits.

I have had a look at some of the other questions on this topic but cannot quite work out the solution to this integral (or prove that there isn't a solution). Is there a way to work out: ...
71 views

### Transforming a Continuous Function

My math is quite limited so please bear with me. I will get to the point: Is there a way to transform a continuous function into a bounded one? In essence I have a normalized Gaussian distribution ...
Let $X$ be a random variable having standard normal distribution. Let $\Phi$ denote its distribution function. Find $$\int_0^\infty \operatorname{Prob} (\Phi(X) \geq u) \; du$$
### Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
I would like your help with proving that for every $0 \leq k \leq n$, $$\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx .$$ I tried to integration by parts and to get a pattern or to ...