Bonus: Discuss the concept of statistical degrees of freedom (5 points)
Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical model with parameter ER". Let O be the parameter that generates the n lid samples X1,..., X, Let I ) be the Fisher information and assume that the MLE is asymptotically normal. Assume that I(C) is a diagonal matrix with positive entries 1/t1,...,1/td. We wish to perform a test for the hypotheses H : 8 - and H:8 + . Let the test statistic...
Q1. a) Explain the term "degrees of freedom" of a mechanical system. Why is this a useful concept? Using suitable assumptions, use a multibody representation of the main moving parts of the human body (rigid bodies and joints) and estimate the number of degrees of freedom. [10 marks]
2. DEGREES of FREEDOM. Calculate the number of degrees of freedom for the mechanism shown. Clearly label all links and joints. OTH Slider
(QUESTION 5] (10 Points) Consider a linear system with three degrees of freedom. In matrix form, the equations of motion for damped free vibrations are given by [M][*]+[C][i]+[K][x]-[o] with (100) [M]- 0 2 0 [kg] 1003) (140 -600 ) [K]=-60 100 -40 [N/m] (0 -40 40 (15 -5 o [C] -1 -5 20 -15 [N.s/m] TO -15 15 Using any method of your choice, find the damping ratio for each mode.
8) The F value for 6 degrees of freedom for the numerator, 24 degrees of freedom for the denominator, and a 0.05 area in the right tail is: a. 2.60 Ob.2.51 O c. 2.78 O d. Cannot answer from given information. QUESTION 9 9) A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for six...
F is a random variable with u = 5 and v = 3 degrees of freedom. What is the probability that F is bigger than .1289?
5. Using the Kolmogorov-Smirnov two-sample test, show that the t statistic with large degrees of freedom can be approximated by the standard normal distribution. How large should the degrees of freedom be? Hint: Do simulations on a large sample.
5. Let X have the T distribution with n degrees of freedom (abbreviated X = T(n)). Show that T2(n) = F(1, n),in other words, T2 has an F distribution with 1 and n degrees of freedom.
true or false? the total area under a t-distribution curve with 5 degrees of freedom is 1
If T has the Student's t distribution with 5 degrees of freedom, find P(T > -0.2). (Hint: try ?pt.)