Range is any number besides 1,2,3,4
Answer/Step-by-step explanation:
(a) The likelihood function to estimate this probability can be written as:
mat[1000, 9800]p9580(1 - p)420
(b) The value of the maximum likelihood estimate of the probability 0.958(By taking log of expression in (a) above)
(c) when the true probability is 98%, then it implies that 9800 of 10,000 bulbs did last over 6500hours.
Therefore, the likelihood is p(9800) = mat[10000, 9800]p9800(1 - p)200
(d) Method of moments estimate is the estimation of all the parameters of the population sample.
(e) The statement is FALSE because estimates by the method of moments are not necessarily sufficient statistics, because sometimes fail to take into account all relevant information in the sample. As in the above question
A * 4 = E........A = E / 4
B / 4 = E........B = 4E
C + 4 = E......C = E - 4
D - 4 = E.......D = E + 4
A + B + C + D = 100
(E/4) + (4E) + (E - 4) + (E + 4) = 100
E/4 + 6E = 100 ....multiply by 4
E + 24E = 400
25E = 400
E = 400/25
E = 16 <===
