Question

Exercise 1. Exponential Random Variable is Memoryless. The time T until a new light bulb burns out is an exponential random variable with parameter λ. Jane turns the light on, leaves the room, and when she returns, t time units later, finds that the bulb is still on, which corresponds to the event A = {T > t}. Let X be the additional time until the bulb burns out. What is the conditional CDF of X, given the event A?

Answer 1

Explanation:

to calculate the conditional CDF of X, given the event A, the conditional PMF of X given A is defined as PX|A(xi)=P(X=xi|A)=P(X=xi and A)P(A),for any xi∈RX. Similarly, we define the conditional CDF of X given A as FX|A(x)=P(X≤x|A).

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