3. (a) Suppose that ri,...,In are a random sample having probability density function C: a Here α is restricted to be positive. Determine the MLE of α (b) Suppose that ri, , Vn are a random sample from a geometric distribution ㄨㄧ Here the parameter 0 < θ < I. Determine the MLE of θ and show carefully that it is an MLE: it does not suffice to solve the score equation.
10 points (bonus) A propositional formula on n variables, P(ri,2,... ,Tn) is satisfiable if there exists an assignment of truth values (true or false) to its variables such that it evaluates to true. (a) Give an algorithm (pseudocode) that, given a formula P determines if it is satisfiable or not. Analyze your algorithm. b) Suppose that we are given a free" algorithm A that, given P and a partial assignment of truth values (that is, some variables are set to...
matlab help, please
my code is here:
%% exercise2
%a
Fs = 8000; % sampling frequency
tn = 0:1/Fs:0.005; % here, bit duration is 0.005s instead of
1/300s
phi1 = 0; phi0 = 0; % phases of the sinusoid
x1 = cos(2*pi*1650*tn + phi1); % tone for binary 1
x0 = cos(2*pi*1850*tn + phi0); % tone for binary 0
xx = [x1, x0]; % FSK signal for ¡°1,0¡±
tt = [tn, tn + 0.005]; % time
figure(1)
plot(tt, xx); %...
> uppas ?, i-.Tn denote a random Sample of size n fron a Gamma with not-the esti unbiased
Let x1,..., Tn be a variable measured for units in a sample with sample variance given by s - a-2)2 T where r r, is the mean of the sample. Let u denote the mean of the population from which 2-1 the sample came. Let yi -xi - 7, for i -1,...,n. How do the values of sz and sy compare to s2 and sz? Prove your result. (More on this in the Computational section of the homework.) Let zi...
First sample average = 4 Second sample average = 9 SS for first sample = 16 SS for second sample = 15 Sample size for first sample = 8 Sample size for second sample = 8 Compute the t-score. Round your answers to 2 decimal places and be sure to include the negative (-) if necessary, in your answer. Enter your response in the space provided here.
First sample average = 3 Second sample average = 8 SS for first sample = 17 SS for second sample = 13 Sample size for first sample = 5 Sample size for second sample = 5 Compute the t-score. Round your answers to 2 decimal places and be sure to include the negative (-) if necessary, in your answer. Enter your response in the space provided here.
3. Let Tn(x) be the degree n Chebyshev polynomial. Evaluate Tn (0.5) for 2 <n < 10, by applying the three-term recurrence directly with x = 0.5, starting with T.(0.5) = 1 and Ti(0.5) = 0.5.
One factory claims that its remote control carts last an average of 320 hours. To verify this average, a sample of 15 carts is taken. If the calculated value falls within a symmetrical range from the 90% average, the factory is satisfied. What conclusion would the company obtain according to this sample? The sample were the following data: 320, 321, 311, 313, 310, 300, 302, 312, 310, 275, 310, 287, 293, 300, 295
Exercise 7. Let Xi, X2, . . . be independent, identically distributed rundorn variables uithEX and Var(X) 9, and let Yǐ = Xi/2. We also define Tn and An to be the sum and the sample mean, respectively, of the random variablesy, ,Y,- 1) Evaluate the mean and variance of Yn, T,, and A (2) Does Yn converge in probability? If so, to what value? 3) Does Tn converge in probability? If so, to what value? (4) Does An converge...