概率论与数理统计1(国外英文资料).docVIP

概率论与数理统计1(国外英文资料) 1.. Slightly. See the textbook exercises refer to the answer. 2. A, B, C for the three event, use A, B, C said the formulae of the following events: the (1) A occurs, and neither B nor C occurs; (2) A and B, the C does not occur; (3) A, B, C occur; (4) A, B, C at least one; (5) A, B, and C do not happen; (6) A, B, C does not occur; (7) A, B, C, at most 2 occur; (8) A, B, C at least 2. [solution] (1) A (2) AB (3) ABC (4) A, B, C= C, B, A, BC, A C, AB, ABC= (5) = (6) (7) BC, A C, AB, C, A, B = = u u u (8) AB, BC, CA=AB, A C, BC, ABC 3.. Slightly. See the textbook exercises refer to the answer. 4. A, B is a random event, and P (A) =0.7, P (A? B) =0.3, P (the). [solution] P (), =1, P (AB), =1, [P (A), P (A, B)] =1? [0.7? 0.3]=0.6? 5. A, B is the two event, and P (A) =0.6, P (B) =0.7, asking: (1) under what conditions does P (AB) take the maximum? The (2) under what conditions does P (AB) take the minimum? The [solution] (1) when AB=A, P (AB) takes the maximum value of 0.6. (2) when A, B=, P (AB) to get the minimum value is 0.3. 6. A, B, C three and P (A), =P (B) =1/4, P (C) =1/3 and P (AB) =P (BC) =0, La P (AC) =1/12, A, B, C at least to have a probability of events. [solution] P (A, B, C) =P (A) +P (B) +P (C)? P (AB)? P (BC)? P (AC) +P (ABC) + + + =? 7.. From the 52 cards to remove any 13 cards, ask 5 spades, 3 hearts, 3 of diamonds, what is the probability of the 2 clubs? [solution] p= 8.. For a five learning group considered the birthday problem: (1) the probability of five peoples birthdays on Sunday; (2) asking five peoples birthdays not on Sundays probability; (3) ask five peoples birthday not all in Sundays probability [solution] (1) set A1={, five peoples birthdays are on Sunday}, the total number of basic events is 75, there are only 1 favorable events P (A1) = = () 5 (also solved by independence) (2) set A2={, five peoples birthdays are not on Sunday}, the number of favorable events is 65, so P (A2) = = () 5 (3) set A3={, five peoples bi