Let W be the exponentially distributed waiting time in minutes for the next metro train to arrive.
If P (W < 2) =1/3, compute P (W > 7 | W ≥ 5).

Solve for .

.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  

But

Who's old now and who is MEMORYLESS?
I still think that the point of this problem was to highlight the memoryless property.
That's why I would have assigned it.
It shows that finding lambda is unnecessary.

But .... are these rhetorical question ....? I'm tempted to say that the answer to both is you - the latter because you've clearly forgotten what the reaction of a typical student would be to your reply (assuming a student has been exposed to that property of the exponential distribution) .....

(But you're right, I should have included it as a throw away footnote ....)

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.