1.2.15. Suppose S is an uncountable set. Is it possible that P({s}) = 0 for every single s ∈ S? Why or why not?
Let S be set of all real numbers from minus infinity to positive infinity.
So probability of having a intezer in that infinite uncountable number of elements is 1/infinity
That is zero..
So it is possible to have that probability be 0
Thanks
1.2.15. Suppose S is an uncountable set. Is it possible that P({s}) = 0 for every...
1.2.14. Suppose S is a finite or countable set. Is it possible that P({s}) = 0 for every single s ∈ S? Why or why not?
Suppose is a subset of the cartesian product of a finite set and uncountable set, anuBis the product two countably infinite sets.What can you say about|A∩B|? What can you say about|P(A∪B)|?
Exercise 3.2.12. Let A be an uncountable set and let B be the set of real numbers that divides A into two uncountable sets; that is, s E B if both {{ : 2 € A and r < s} and {x : x € A and x > s} are uncountable. Show B is nonempty and open. T
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, In a standard set of double-six dominoes, there is exactly one domino for every possible (unordered) pair of numbers from 0 to 6 (including doubles, i.e. a domino with two fives.) A "hand" of dominoes is another word for a set of dominoes. (a) How many dominoes are there (show your work)? (b) How many five-domino hands are there? (c) How many five-domino hands contain no domino with a 0? (d) How many five-domino hands contain at least one...
Let p be a prime >0. Prove that 12,23 (21) gives a set of different remainders modulus p. Also prove that for every number a with pla, a is congruent to one and only one of the element in the previous set. Let p be a prime >0. Prove that 12,23 (21) gives a set of different remainders modulus p. Also prove that for every number a with pla, a is congruent to one and only one of the element...
Let S the set of all points x+0 of RAn. Suppose that r=1x11 and be f a vector field defined in S by the equation f(x)=r^px Being p a real constant. Find a potencial function for f in S Let S the set of all points x+0 of RAn. Suppose that r=1x11 and be f a vector field defined in S by the equation f(x)=r^px Being p a real constant. Find a potencial function for f in S
Suppose the program counter (PC) is set to 0x30002000. Is it possible to use the jump (j) MIPS assembly instruction to jump directly to the instruction at 0x50003000? If yes, write the corresponding assembly instruction(s). If not, explain why and give other MIPS instruction(s) that can jump to this target address. (For this problem, assume that the instruction memory starts from 0x00000000 and goes to 0xFFFFFFFF.)
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Suppose A and B are two event with P [A] 2 and P[B] . Is it possible that An B Why? 0?