A random sample of n bike helmets manufactured by a company is selected. Let x = the number among the n that are flawed, and let p = P flawed). Assume that only x is observed, rather than the sequence of Ss and Fs. (a) Derive the maximum likelihood estimator of p. If n= 20 and x = 3 what is the estimate?
(b) Is the estimator of (a) unbiased?
(c) If n= 20 and x = 3 what is the mle of the probability (1 - p)^5 that none of the next five helmets examined is flawed?

a

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

the answer is a.

135 and 80

step-by-step explanation:

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