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Exercise 1 Prove that the variance of a geometric random variable X with parameter p is: (16) 9-1/14 p² Hint Recall that Var[X] = E[X²] - E[X]2. Use Equation (8) to find E[X²]. Var[X] =

Exercise 1 Prove that the variance of a geometric random variable X with parameter p is: (16) 9-1/14 p² Hint Recall that Var[X] = E[X²] - E[X]2. Use Equation (8) to find E[X²]. Var[X] =

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.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 63E
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Exercise 1
Exercise 1 Prove that the variance of a geometric random variable X with parameter p is: Var[X] =2 (16) Hint Recall that Var[X] = E[X²] – E[X]². Use Equation (8) to find E[X²].
Transcribed Image Text:Exercise 1 Prove that the variance of a geometric random variable X with parameter p is: Var[X] =2 (16) Hint Recall that Var[X] = E[X²] – E[X]². Use Equation (8) to find E[X²].
Theorem 2.1 If X has a geometric distribution with parameter p, then 1 Р Proof Write E[X] = E[X]= = 4 ∞ Σxq-¹p x=1 ∞ =²q² x=0 Using Equation (4) with a = q = 9 p Р en (14) (15) To give a numerical example, the average number of rolls of a pair of dice until the first roll of seven is 6.
Transcribed Image Text:Theorem 2.1 If X has a geometric distribution with parameter p, then 1 Р Proof Write E[X] = E[X]= = 4 ∞ Σxq-¹p x=1 ∞ =²q² x=0 Using Equation (4) with a = q = 9 p Р en (14) (15) To give a numerical example, the average number of rolls of a pair of dice until the first roll of seven is 6.
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