Let X₁, X2, X3, X4, X5 be an independent and identically random variables following a Binomial distribution with probability of success and 5 independent trials. a) What is the expected value of T = [(X² + X₁)? b) Find the probability distribution function of Y = Σ₁=1 X₁. Find the mean and variance of Y = ₁1X₁- c)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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b) What is the mean of the statistic Y = 11101 ?
10
a
c) Find the probability distribution function of Y = [Xj.
10
d) What is the probability that Y = 10₁ X₁ is at least 3?
i=1
2) Let X₁, X2, X3, X4, X5 be an independent and identically random variables following a
Binomial distribution with probability of success and 5 independent trials.
a) What is the expected value of T = []=₁(X₁² + X₁)?
Find the probability distribution function of Y = Σ₁=1 X₁.
Find the mean and variance of Y = ₁=₁ X₁.
b)
c)
d) What is the P(0 < Y ≤ 3)?
3) Suppose that X₁, X₂,..., X100 is a random sample from a normally distributed
25 and variono ² - 26 IFV-¹100 y
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nnnulation with mann
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c2
21°C
d
Transcribed Image Text:b) What is the mean of the statistic Y = 11101 ? 10 a c) Find the probability distribution function of Y = [Xj. 10 d) What is the probability that Y = 10₁ X₁ is at least 3? i=1 2) Let X₁, X2, X3, X4, X5 be an independent and identically random variables following a Binomial distribution with probability of success and 5 independent trials. a) What is the expected value of T = []=₁(X₁² + X₁)? Find the probability distribution function of Y = Σ₁=1 X₁. Find the mean and variance of Y = ₁=₁ X₁. b) c) d) What is the P(0 < Y ≤ 3)? 3) Suppose that X₁, X₂,..., X100 is a random sample from a normally distributed 25 and variono ² - 26 IFV-¹100 y E collab-recording (....mp4 collab-recording (....mp4 nnnulation with mann 661f205960a9d86....mp4 c2 21°C d
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