Let the random variables x and y have joint distribution f(x, y) = (2x + y)/30, x = 1,2 ; y = 1,2,3. a)find the marginal pdf's f1(x) of x and f2(y) of y. b)are x and y independent? justify your answer.

Emma will roll two number cubes labeled 1 through 6. she will record the sum of the two numbers after each roll. she will roll the two cubes 540 times. how many times should emma expect the sum to equal 5?

Ben is three times as old as samantha, who is two years older than half of michel's age. if michel is 12. how old is ben?

Which value would be a solution for x in the inequality 47-4x< 7