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Exercise 26 Compute the expected values of random variables with Bernoulli(p), Binom(n,p), Geom(p) and NegBi- nom(k,p) distributions, respectively, in terms of the unknown parameters. Show your computations. Let X be a discrete random variable. (i) Prove that Var(X) = E(X²) –- (EX)². Hint: Use the definition of the variance, the binomial formula, and the facts you know about the expected value. Notice that EX is a real number and can be treated like a constant. (ii) Prove that Var(aX +b) = a²Var(X), for any a, be R.

Exercise 26 Compute the expected values of random variables with Bernoulli(p), Binom(n,p), Geom(p) and NegBi- nom(k,p) distributions, respectively, in terms of the unknown parameters. Show your computations. Let X be a discrete random variable. (i) Prove that Var(X) = E(X²) –- (EX)². Hint: Use the definition of the variance, the binomial formula, and the facts you know about the expected value. Notice that EX is a real number and can be treated like a constant. (ii) Prove that Var(aX +b) = a²Var(X), for any a, be R.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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Exercise 26 Compute the expected values of random variables with Bernoulli(p), Binom(n,p), Geom(p) and NegBi- nom(k,p) distributions, respectively, in terms of the unknown parameters. Show your computations. Let X be a discrete random variable. (i) Prove that Var(X) = E(X²) – (EX)². Hint: Use the definition of the variance, the binomial formula, and the facts you know about the expected value. Notice that EX is a real number and can be treated like a constant. (ii) Prove that Var(aX + b) = a²Var(X), for any a, b e R.
Transcribed Image Text:Exercise 26 Compute the expected values of random variables with Bernoulli(p), Binom(n,p), Geom(p) and NegBi- nom(k,p) distributions, respectively, in terms of the unknown parameters. Show your computations. Let X be a discrete random variable. (i) Prove that Var(X) = E(X²) – (EX)². Hint: Use the definition of the variance, the binomial formula, and the facts you know about the expected value. Notice that EX is a real number and can be treated like a constant. (ii) Prove that Var(aX + b) = a²Var(X), for any a, b e R.
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