PHP:

```
It is given that at a certain bank there's 50-50 chance that when you
enter there's:
- no one waiting in line
- there's one man waiting, in which case the waiting time is
exponentially distributed.
What is the CDF of the total waiting tine?
Instruction:
Let X be the total waiting time, Y the number of people waiting.
For x>=0, use the total probability theorem for the CDF of X
Notice that X is not discrete nor continuous, but a mix of both.
```

So, by the law of total probability,

P(X<=x) = P(X<=x|Y=1)P(Y=1) + P(X<=x|Y=0)P(Y=0)

Am I right so far? If I am right, then what is P(X<=x|Y=1)? Are the two variables independent?

Thanks!