Stats Help for College-level Students

Probability

Find the probability for the various situations

Expected value in a Poisson process

Expected value in a Poisson process Don't know how to compute the expected value (see attached file).

This problem deals with finding the least squares estimate of a parameter theta.

Let Y1 and Y2 be independent random variables, with means theta, and 3*theta, respectively. Find the least squares estimate of theta. (See attachment)

Statistics

Please your how you go to answer thanks. 1) The FMA Company has designed a new type of 16 lb. bowling ball. The company knows that the average man who bowls in a scratch league with the company's old ball has a bowling average of 155. The variance of these averages is 100. The company asks a random sample of ...continues

Regression Analysis of 5 UK Stocks-Barclays, HSBC, Astra, Reuters, Marks & Spencer

Based on a period of 7 years, Run the regression analysis in Excel for 5 UK stocks. Use the FTSE-100 index to calculate the expected return on the market. 1) Use a 5% significant level, to test for the significance of the intercept and slope. Comment on the results. 2) Estimete the total risk explained by the market and ...continues

Joint Probabilities

Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let T = Z / √ (V/n) Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)

Probabilities

Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let U = (X/m) / (Y/n) a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom). b) Find the density of V = U / (1+U)

Probabilities

Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2. a) Find the joint density of Y1 and Y2. b) Find the marginal density of Y1.

Probabilities

Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2. a) Find the joint density of Y1 and Y2 b) Find the marginal density of Y1 and Y2 (The distribution of Y2 is known as the Cauchy distribution).

Five step process for calculating probabilities of events with illustrative example

What are the five steps for calculating probabilities of events? Please apply these steps to an example.