Determine whether f is a function from the set of all bit strings to the set of integers if (a) f(S) is the position of a 0 bit in S. (b) f(S) is the number of 1 bits in S.

(a) Not a function, because a string can be assigned to more than one value.

(b) Function

(c) Not a function, because the function does not assign an integer to every string.

Step-by-step explanation:

Definition:

A function f from A to B has the property that has each element of A has been assigned to exactly one element of B.

Solution

            A =Set of all bits strings

              B= Z

(a) Given: f(S) ={position of a 0 bit in S}

     f is not a function,because a string can be assigned to more than one value.

     for example if S = 001, then f(S) =1 and f(S) =2,because S =001

contain a 0 in the first and second position.

Moreover there are also strings that do not get assign to an integer.For example,the string S= 111111 does not get assign by f,because S does not contain any 0's .

b) Given:f(S) ={number of 1 bits in S}

    f is defined for all strings and  the action f maps every element of A to exactly one element in Z,thus f is a function.

c)Given:

f(S) =i if the ith bit of S is the first 1 in the string

f(S)= 0 if S is the empty string

f is not a function because the string does not assign an integer to every string. More precisely,no integer are assigned to all string not containing a 1.

For example:

if S=00111,then f(S) =3.

if S=000000,then f(S) is not defined.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497