I'm studying for P and I can't figure out this problem. I'm stumped on why it's distributed as it is.
Basically we are given that T is an exponential with mean 5. Simple enough. X = max(3,T). Okay, so X is 3 when T is less than 3, and X is T when T is greater than 3. I'm supposed to find E[X]. Obviously, it's going to be the sum of the expected values for the two pieces. I correctly wrote the expected value for the second piece:
Which is
But I would have thougt that the expected value for the first piece would just be three. After all that is the only value that X can take on in that range... But it is apparently this.
Could someone explain this to me?
Basically we are given that T is an exponential with mean 5. Simple enough. X = max(3,T). Okay, so X is 3 when T is less than 3, and X is T when T is greater than 3. I'm supposed to find E[X]. Obviously, it's going to be the sum of the expected values for the two pieces. I correctly wrote the expected value for the second piece:
Which isBut I would have thougt that the expected value for the first piece would just be three. After all that is the only value that X can take on in that range... But it is apparently this.
Could someone explain this to me?
Exam P Prep question: Why is this distribution confusing me?
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