(Solution) - Let X be the waiting time in minutes until a -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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Let X be the waiting time (in minutes) until a student's friend arrives. Suppose that X has density
fx(x) = 1/3 e-x/3
for 0 < x,
and fx{x) = 0 otherwise.
a. Find P(3 ? X v 6).
b. Find the CDF Fx(x).
c. Find P{X ? 24).
d. Find P(X ? -3).
e. Find P(3 ? X ? 12).
f. Find P(X < 300).
g. Graph the density fx(x).
h. Graph the CDF Fx(x).