То были цветочки, теперь пошли ягодки...
Без лекций здесь делать нечего...
a) i) 3/2, 9/20; ii) 1/2; iii) 7/27;
b) a = 1/4, b = root of 8;
b) a = 1/4, b = root of 8;
i) watch the video;
ii) 0;
iii) 1/20;
ii) 0;
iii) 1/20;
i) 0.2929 (4 d.p.);
ii) 0.3614 (4 d.p.);
iii) 0.3712 (4 d.p.);
ii) 0.3614 (4 d.p.);
iii) 0.3712 (4 d.p.);
a) watch the video;
b) due to the symmetry;
c) 20;
d) 2p-1;
e) 0.296;
b) due to the symmetry;
c) 20;
d) 2p-1;
e) 0.296;
a) 5/32;
b) watch the video;
c) 3.47;
b) watch the video;
c) 3.47;
a) i) 0.3413; ii) 0.4772;
b) i) 0.0228; ii) 0.8413;
c) 68;
d) 178;
b) i) 0.0228; ii) 0.8413;
c) 68;
d) 178;
a) 176, 24;
b) 82%;
b) 82%;
a) 12.48;
b) 18.84;
c) 4.935;
b) 18.84;
c) 4.935;
i) 0.4815 (4.d.p);
ii) 0.0516 (4 d.p.);
iii) 0.2283 (4 d.p.);
ii) 0.0516 (4 d.p.);
iii) 0.2283 (4 d.p.);
i) 1.474h;
ii) 0.7781;
iii) 0.8849;
ii) 0.7781;
iii) 0.8849;
i) 8.34, 0.68;
ii) 0.2619 (4 d.p.);
ii) 0.2619 (4 d.p.);
i) 5.62 (2 d.p.);
ii) 67;
ii) 67;
i) 0.1174 ( 4 d.p.);
ii) 7;
iii) 0.1724 (4 d.p.);
ii) 7;
iii) 0.1724 (4 d.p.);
a) 6.5;
b) 0.4648;
b) 0.4648;
a) 0.4482 (4 d.p.);
b) 0.9545;
b) 0.9545;
a) 0.3632;
b) 0.8472;
b) 0.8472;
a) 0.0174;
b) 0.1492;
b) 0.1492;
a) 6, 0.0045;
b) 0.0125;
b) 0.0125;
0.0281;
a) 0.3679 (4 d.p.);
b) 0.2325 (4 d.p.);
b) 0.2325 (4 d.p.);
2/5;
The second option is more efficient in the context of the problem.
0.8365;
3/5;
exp(-10^y)*10^y*ln(10), for all real values of y.
1/y, for all values of y between 1 and e;
watch the video;
a) 0.9114 (4 d.p.), 0.7714 (4 d.p.);
b) 0.2449 (4 d.p.);
b) 0.2449 (4 d.p.);
0.2765 (4 d.p.);
a) k = 1/4, p = 25/72;
b) -0.0286 (4 d.p.);
b) -0.0286 (4 d.p.);
Cov = -2.
Corr can't be calculated, Var(1/(1-X)) doesn't exist;
Corr can't be calculated, Var(1/(1-X)) doesn't exist;
0.8413;
a) watch the video;
b) -0.2731 (4 d.p.);
c) Doesn't exist;
d) 0.775;
b) -0.2731 (4 d.p.);
c) Doesn't exist;
d) 0.775;
a) k = 3.5, uniform distribution;
b) 0.6;
c) 2.25, 0.5208 (4 d.p.);
b) 0.6;
c) 2.25, 0.5208 (4 d.p.);
a) watch the video;
b) i) 2; ii) 2; iii) ln(4); iv) ln(100);
c) i) 0.3935; ii) 0.4509 (4 d.p.);
b) i) 2; ii) 2; iii) ln(4); iv) ln(100);
c) i) 0.3935; ii) 0.4509 (4 d.p.);
a,b) watch the video;
c) 2.975;
d) 1/2*sigma^2, 34/64*sigma^2;
e) T1 is more efficient due to the lower variance;
c) 2.975;
d) 1/2*sigma^2, 34/64*sigma^2;
e) T1 is more efficient due to the lower variance;
a) b/2;
b) watch the video;
b) watch the video;
a) i) 97/30; ii) watch the video;
b) watch the formula in the video;
b) watch the formula in the video;
watch the video;
i) watch the video;
ii) S is the best, T1 is the worst;
ii) S is the best, T1 is the worst;
(y1+3y2)/10; var = 1/10;
watch the video;
Both estimators are n/(x1+x2+...+xn);
They are asymptotically unbiased;
They are asymptotically unbiased;
i) watch the video;
ii) (X+Y)/4 is the best estimator;
iii) 0.9084 (4 d.p.);
ii) (X+Y)/4 is the best estimator;
iii) 0.9084 (4 d.p.);
a) var = 3/80*Theta^2;
b) watch the video;
c) MLE = max{Xi}, MME = 4/3*(x1+x2+...+xn)/n;
b) watch the video;
c) MLE = max{Xi}, MME = 4/3*(x1+x2+...+xn)/n;
watch the video;
i) Theta/2;
ii) 3.27; I wouldn't trust this estimate;
ii) 3.27; I wouldn't trust this estimate;
5/8;
i) root of sample mean;
ii) (sample mean)^(3/2);
ii) (sample mean)^(3/2);
a) watch the video;
b) (1-1/delta)*1/delta;
b) (1-1/delta)*1/delta;
ii) y = 1.03x + 3.25;
iii) 6.5 kg;
iv) no, I wouldn't;
iii) 6.5 kg;
iv) no, I wouldn't;
ii) r = 0.8049 ( 4 d.p.), moderate correlation;
iii) y = 2.74x - 2.64;
iv) 11, I wouldn't trust;
iii) y = 2.74x - 2.64;
iv) 11, I wouldn't trust;
1b) negative;
1c) yes;
2a) watch the video;
1c) yes;
2a) watch the video;
watch the video, it is a mistake in the task;
it is better to watch the video!
1b) i) y = -1.28x + 219; ii) x = -0.693y + 160;
2b) r^2 = 1;
2b) r^2 = 1;
Correct Answer: C
Correct Answer: C
Correct Answer: B
Correct Answer: C
Correct Answer: C
Correct Answer: C
Correct Answer: B
Correct Answer: B
Correct Answer: E
Correct Answer: C
Correct Answer: A
Correct Answer: A
Correct Answer: A
Correct Answer: A
Correct Answer: A
Correct Answer: A
Correct Answer: A
Correct Answer: A
Correct Answer: A
