1) Let X₁, X₂,..., X20 be a random sample from a population X with density f(x; 0) = {0* (1 - 0)¹-*, x = 0,1. 0, otherwise where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0 = to be tested against H₁: p < 1/1/ i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error? ii) If He is rejected when 20, X. ≤ 6. then what is the probability of type I error?

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1.STATISTICAL INFERENCE

1) Let X₁, X₂, ..., X20 be a random sample from a population X with density
f(x;0) = {0* (1-
(0*(1 − 0)¹−*, x = 0,1.
otherwise
where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0 = to be tested against
H₁: p<1/1
i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error?
ii) If Ho is rejected when Σ2₁ X₁ ≤ 6. then what is the probability of type I error?
Transcribed Image Text:1) Let X₁, X₂, ..., X20 be a random sample from a population X with density f(x;0) = {0* (1- (0*(1 − 0)¹−*, x = 0,1. otherwise where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0 = to be tested against H₁: p<1/1 i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error? ii) If Ho is rejected when Σ2₁ X₁ ≤ 6. then what is the probability of type I error?
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Step 1

X~Ber(θ)

Farmula used

nCr=r!/(n!(n-r)!)

r!=r(r-1)x..3×2×1

 

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