Geometric Probability Distribution, Expected ValuesLet X ∼ Geometric ( θ ), and let Y = min ( X , 100 ). Compute (a) E(Y) and (b) E ( Y − X ).I know that the Geometric distribution is ( 1 − θ ) k − 1 θ and I also know how to calculate expected value but I'm confused about what it means that Y = min ( X , 100 )?

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Geometric Probability Distribution, Expected ValuesLet   X  ∼ Geometric   (  θ  ), and let   Y  =  min  (  X  ,  100  ). Compute (a) E(Y) and (b)   E  (  Y  −  X  ).I know that the Geometric distribution is   (  1  −  θ      )          k      −      1        θ and I also know how to calculate expected value but I&#039;m confused about what it means that   Y  =  min  (  X  ,  100  )?

emerhelienapj · Accepted Answer

Step 1  ∀  ω  ∈  Ω  ,    Y  (  ω  )  =      {                            X          (          ω          )                          if                          X          (          ω          )          ⩽          100                                      100                          if                          X          (          ω          )          &amp;gt;          100                        Step 2  E  [  Y  ]  =  100    P  [  X  &amp;gt;  100  ]  +      ∑          k      ⩽      100        k    P  [  X  =  k  ]

Let X~ Geometric (theta), and let Y=min(X, 100). Compute (a) E(Y) and (b) E(Y-X)

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