i) Let X ~Binom(100, 1/4 ). Find a, b 2 R so that Y = aX + b has expected value 0 and variance 1. (ii) Let X1,X2, . . . independent random variables with Bernoulli( 1/3 )‐distribution. Let n Sn := Σ Xi. i=1 Find a, b 2 R so that Y = aS20 + b has expected value 0 and variance 1.
i) Let X ~Binom(100, 1/4 ). Find a, b 2 R so that Y = aX + b has expected value 0 and variance 1. (ii) Let X1,X2, . . . independent random variables with Bernoulli( 1/3 )‐distribution. Let n Sn := Σ Xi. i=1 Find a, b 2 R so that Y = aS20 + b has expected value 0 and variance 1.
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.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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i) Let X ~Binom(100, 1/4 ). Find a, b 2 R so that Y = aX + b has
(ii) Let X1,X2, . . . independent random variables with Bernoulli( 1/3 )‐distribution. Let
n
Sn := Σ Xi.
i=1
Find a, b 2 R so that Y = aS20 + b has expected value 0 and variance 1.
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