A fishpond contains 20 orange fish and 10 green fish. A sample of five fish is taken (withoutreplacement) from the pond. Let X denote the number of orange fish in the sample.(i) State the type of distribution of X, and write down its mass function.(ii) Hence find P(X = 2).(iii) If the sample contains at least four orange fish, how likely is it to contain only orangefish?

Let X = b(16,- find E(4- 3x) and distribution function.

Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n). Is this an exponential distribution?  (This question was rejected this morning. I did double check and there is no missing info with this question.)

For a football game in the National Football League, let y = difference between the number of points scored by the home team and the away team (so y > 0 if the home team wins). Let x bet the predicted difference according to the Las Vegas betting spread. For the 768 NFL games played between 2003 and 2006, output follows. Predictor Coefficient SE Coef T P Constant -0.4022 0.5233 -0.77 0.442 BP 1.0251 0.0824 12.44 0.000 (a) We wish to test the null hypothesis that the Las Vegas predictions are unbiased. This will correspond with ? = 0 and ? = b) Based on the results shown in the table, is there much evidence that the sample fit differs from the model ?y = ? + ?x, with values of alpha and beta above? Why?

A certain process for producing an industrial chemical yields a product containing two predominant types of impurities. For a certain volume of sample from this process, let X1 denote the proportion of impurities in the sample and let X2 denote the proportion of type I impurity among all impurities found. Suppose the joint distribution of X1 and X2, after investigation of many such samples, can be adequately modeled by the following function: (see picture) a. Calculate the probability that X1 is less than 0.5 and that X2 is between 0.4 and 0.7. b. Show that these random variables are independent.

Please help me answer (d) and (e).

Ql: (): Let Y,.,Y4 be order statistics of a random sample of size 4 from Exponential (10). Find g(y,), g(y1,Y3)and P(Y, > 100).

P(z>2) =?

Let X1, . . . , Xn a random sample from a Uniform distribution on the interval [0, 2θ + 1].(a)  Find the MLE of θ.(b) Find the MLE for the variance of the distribution of Xi.

2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).