exponential random variable measured
Jenny and Peter plan to join a zoom meeting at 1pm. The time Jenny
joins, X, is uniform from 1pm to 1:10pm. The time Peter joins, Y , is an exponential random variable measured in minutes starting at 1pm, with λ = 1/4.
1. (3pt) Find the chance that Jenny joins the meeting before Peter.
2. (3pt) Find the density function for Z, the maximum of X and Y .
3. (4pt) Peter intends to record the meeting, and starts the recording T minutes after they have both joined the meeting (at time Z). T is exponential (1/4) independent of Z.
Find P(T + Z > 11).
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