Question-92

Geometric Distribution

Let \(X, Y, Z \sim \text{i.i.d. Geometric}\left(\dfrac{1}{2}\right)\). Define a new random variable \(U = \text{min}(X, Y, Z)\). What is the value of \(\dfrac{1}{P(U \geq 3)}?\)

If \(X \sim \text{Geomteric}(p)\), then \(P(X = k) = p (1-p)^{k-1}\), where \(k=1,2,3, \ldots\)

64