Let's assume that during a phone call we charge a fee every one minute. Time of phone calls is defined by exponential distribution with a parameter of 1. Please calculate the average length of phone call and the average cost of phone call ($1 per minute).
From the definition, it sounds like it's a problem to be solved by the Poisson distribution. How to estimate average 'ticks' during the phone call?
No, it is an exponential distribution of phone call lengths. You get $1$ if the call lasts $0-1$ minute, $2$ if it lasts $1-2$ minutes and so on. You can find the number of calls in each interval by subtracting the cumulative distribution function at those points.