- #1
quacam09
- 16
- 0
Hi all,
Could you please answer my following question related to an exponential random variable? Thank you.
Let X represent the waiting times at a telephone in an office. Assume that X is an exponential random variable with parameter λ: P(X < t) = 1 - e^{-λ*t}
At each time when the telephone rings, a staff at the ofice will toss up a coin. If the coin comes up a tail, she will pick up the phone. If the coin comes up a head, she finishes her job.
Let Y represent the outcomes of each toss. Y = 0 if the coin comes up a tail; Y = 1 if the coin comes up a head. Asume that Y is a random variable. P(Y=0) = 1-p; P(Y = 1) = p where p is a constant (0<= p <= 1).
Let T be the time that she finishes her job.
Is it correct? P(T < t) = ( 1 - e^{-λ*t} ) * p
Could you please answer my following question related to an exponential random variable? Thank you.
Let X represent the waiting times at a telephone in an office. Assume that X is an exponential random variable with parameter λ: P(X < t) = 1 - e^{-λ*t}
At each time when the telephone rings, a staff at the ofice will toss up a coin. If the coin comes up a tail, she will pick up the phone. If the coin comes up a head, she finishes her job.
Let Y represent the outcomes of each toss. Y = 0 if the coin comes up a tail; Y = 1 if the coin comes up a head. Asume that Y is a random variable. P(Y=0) = 1-p; P(Y = 1) = p where p is a constant (0<= p <= 1).
Let T be the time that she finishes her job.
Is it correct? P(T < t) = ( 1 - e^{-λ*t} ) * p