(20 Poinby) Let Y ~ Bernoulli be independent Bernoulli i1,2. n be independent Bernoulli ran dom v...
5.4-9. Let X and Y, with respective pmfs f(x) and g(y), be independent discrete ran- dom variables, each of whose support is a subset of the nonnegative integers 0, 1,2, Show that the pmf of W - X + Y is given by the convolution formula x=0 Hint: Argue that h(w) P(Ww) is the probability of the w 1 mutually exclusive events (x, y-w-x), 0,,..., w.
1. Let Xi,X2,... .X, be independent identically distributed N( 5,4 ran dom variables Find (use tables or software) t such that (a) P(X-51 > t) = .95 1-2-) >t) = .05 (c) P0% (X (d) P(LL52 *)2 > t) > t) .95 .95 where 82- Σ(x,-x)2
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent ran- dom variables, we can find joint probabilities by multiplying together th ndividual probabilities. For example This should remind you the discussion on statistical independence of random variables that can be found in the course book (see page 22) Answer the following questions a...
12 marks Let independent random samples of sizes n and n2 be taken respectively from two normal distributions with unknown means 1 and 2 and unknown variances oand o. Denote the two samples by . . ,Jn, and y,... , yn2: Which have means T and T, and sample variances s and s2, respectively (a) 4 marks Show that when of = o2, the likelihood ratio test statistic for testing Ho 12 against H 2 can be written as T2...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
DISPLAY A Descriptives Descriptive Statistics N Minimum Maximum Mean Std. Deviation 1.376 72.673 EXPENDITURE 48 3.656 9.774 5.946 SAT 48 854.000 1107.000 970.563 Valid N (listwise) 48 Model Summary Model R R Square Adjusted R Std. Error of Square the Estimate 65.492 453 205 188 a Predictors: (Constant), EXPENDITURE ANOVA Model F Sig. Sum of df Mean Square Squares 50920.77 11.872 0.001 4289.197 1 Regression 50920.77 1 Residual 197303.00 46 Total 248223.80 47 a Predictors: (Constant), EXPENDITURE b Dependent Variable:...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
If can't complete it all, I can post more questions just let me
know!!
There is an old saying in golf: "You drive for show and you putt for dough. "The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 69 money winners on the PGA tour in 1993 are examined. The average number of putts per hole for...