Exercise 4.50. suppose an alarm clock has been set to ring after t hours, where t ∼ exp(1/3). suppose further that your friend has been staring at the clock for exactly 7 hours and can confirm that it has not yet rung. at this point, your friend wants to know when the clock will finally ring. calculate the conditional probability that she needs to wait at least 3 more hours, given that she has already waited 7 hours. more generally, calculate the conditional probability that she needs to wait at least x more hours, given that she has already waited 7 hours

13cm

step-by-step explanation:

(apex)

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.