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
By DeMoivre's theorem,
where . , so the 4th roots are
THE ANSWER IS 0.63 . i think
Answer: 50.24 cm^2
Step-by-step explanation:
This can be translated to:
An old coin is kept in a cubic box in such a way that the outline of the coin touches the 4 walls of the box, if the base of the box has a perimeter of 24 cm. What is the area of the coin?
The fact that the coin touches the interior of the box means that the diameter of the coin is equal to the side lenght of the box.
The perimeter of the box is 24 cm, and the perimeter of a square is equal to:
P = 4*L
where L is the side lenght of the square.
24 cm = 4*L
L = 24cm/4 = 8cm
Now we know that the diameter of the coin is 8cm
Now, the area of a circle (the coin) is equal to:
A = 3.14*(d/2)^2
where d is the diameter, so we have:
A = 3.14*(4cm)^2 = 50.24 cm^2