Let x1 and x2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. let y1 = (x1/r1)/(x2/r2) and y2 = x2. (a) find the joint pdf of y1 and y2. (b) determine the marginal pdf of y1 and show that y1 has an f distribution. (this is another, but equivalent, way of finding the pdf of f.)

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 3 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30∘c on monday, but decreased at a constant rate in the next 3 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.

Look at the hyperbola graphed below. the hyperbola gets very close to the red lines on the graph, but it never touches them. which term describes each of the red lines? o o o o a. asymptote b. directrix c. focus d. axis

Which of the following is closest to 32.9 x 7.5? a: 232 b: 259 c: 220 d: 265