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'Example 7-37. A random variable X assumes the value M, 2, ... with probabilities U1, Uz, ... respectively. Show that E u;e(^,)*; ^; > 0, Eu; = 1 Pk = k!

'Example 7-37. A random variable X assumes the value M, 2, ... with probabilities U1, Uz, ... respectively. Show that E u;e(^,)*; ^; > 0, Eu; = 1 Pk = k!

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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: 'Example 7-37. A random variable X assumes the value 1, 12, ... with probabilities U1, Uz ... respectively. Show that 1 u; e» (^;)* ; ^; > 0, Du; = 1 j=0 Pk k! =D0
Transcribed Image Text:: 'Example 7-37. A random variable X assumes the value 1, 12, ... with probabilities U1, Uz ... respectively. Show that 1 u; e» (^;)* ; ^; > 0, Du; = 1 j=0 Pk k! =D0
is a probability distribution. Find its generating function and prove that its mean equals E (X) and variance equals V(X) + E(X).
Transcribed Image Text:is a probability distribution. Find its generating function and prove that its mean equals E (X) and variance equals V(X) + E(X).
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