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Homework 2Probability Theory and Mathematical Statistics Spring 2019

1.（2）

Answer:


2.（5）

Answer:

(a) According to the exercise 3, (a)A=(A∩B) (A∩B')∪

since (A∩B),(A∩B') are mutually exclusive, we get

P(A)=P(A∩B)+P(A∩B')

and P(A)，P(A∩B)，P(A∩B')≥0

therefore P(A)≥P(A∩B)

(b) According to the exercise3, (a)A=(A∩B) (A∩B')∪

(b)A B=(A∩B) (A∩B') (A'∩B)=A (A'∩B)∪ ∪ ∪ ∪

since A, (A'∩B) are mutually exclusive

P(A B)=P(A)+P(A'∩B)∪

and P(A B), P(A), P(A'∩B)≥0∪

therefore P(A B)≥P(A)∪ ,which also means that P(A)≤P(A B)∪


3.（8）

Answer:


4.（12）

Answer:


5.（35）


6.（39）

Answer:


7.（41）

Answer:

a)The ten elements of the sample space S are

(H,1) ， (H,2) ， (H,3) ， (H,4) ， (H,5) ， (H,6) ， (T,T,T) ， (T,T,H) ，(T,H,T)， (T,H,H).

b)The elements of S corresponding to event A that exactly one head

occurs are

(H,1) ，(H,2)， (H,3) ，(H,4) ，(H,5) ，(H,6) ，(T,T,H) ，(T,H,T).

c)The elements of S corresponding to event B are

(H,5)， (H,6) ，(T,T,T)， (T,T,H)， (T,H,T).


8.（47）

Answer:

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