Aflea of negligible size is trapped in a large, spherical, inflated beach ball with radius r. at this moment, it is equally likely to be at any point within the ball. let x be the distance of the flea from the center of the ball. using the fact that the volume of a sphere of radius r is 4tr /3, for x, find (a) cumulative distribution function f. ( the probability density function f. (c) expected value. d) . the variance.

12/11c

or

12

c

11

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.