Answer to Question #63548 in Statistics and Probability for Bright

Question

The exponential distribution with rate parameter μ > 0 is a continuous distribution on [0, ∞) with density

f(t) = μ exp(−μt), t > 0

1. Compute the cumulative distribution function defined by

F(t) := P(X ∈ [0,t]).

2. Compute P(s < X ≤ t).

3) Find P( X∈ [1,2] ∪[3,4] ).

4) Compute the conditional probability P (X ∈ [3, 4] | X ∈ [1, 4] )

5) Compute the conditional probability P (X > t + s | X > s ) for s, t ≥ 0.

6) Find the mean of the exponential distribution with rate parameter μ > 0.