求 各位大神帮忙解决下这些题1.Let U and V be independent, continuous uniform random variables on the interval [1; 5]. Find
P[min{U; V}  < 2 | max{U; V }> 2]
A. 3/8 B. 2/5 C. 3/5 D. 5/8 E. 2/3
2.A fair 6-sided die is rolled 1,000 times. Using a normal approximation with a continuity correction,
what is the probability that the number of 3's that are rolled is greater than 150 and less than 180?
A. 0.78 B. 0.81 C. 0.84 D. 0.88 E. 0.95
3.Suppose that X1;……;X5 are i.i.d., uniform random variables on the interval (3; 6). Let X
denote the average of X1 through X5, and let  u and b  
denote the standard deviation and mean of X
. Find the probability that the minimum and maximum of X1; ……:X5 both differ from  u
by less that  b
.A. 0.00001 B. 0.00032 C. 0.00057 D. 0.00083 E. 0.00115
4.In a blind tasting of wines from Bordeaux and Napa valley, a wine expert has a 90% chance of correctly
identifying that a wine is from Bordeaux and an 80% chance of correctly identifying a wine from Napa
valley. If 60% of the wines at the tasting are from Napa, what is the probability that a randomly
selected wine is from Napa valley, given that the wine expert said that it was from Napa valley?
A. 0.60 B. 0.80 C. 0.83 D. 0.90 E. 0.92
5.For a random variable X, let g(X) be given by g(X) = E|X -m(X)|, where m(X) is the median of
X. Find g(X) for a Poisson random variable with mean 1.5.
A. 0.5 B. 0.7 C. 0.9 D. 1.0 E. 1.1
6.A company insures 2 machines for maintainance. In a given year, each machine will require main-
tainance with probability 1/3, and if maintainance is required, the cost will be a uniform random
variable between $0 and $4,000. If the insurance policy has an annual payment limit of $6,000 for both
machines combined, what is the expected annual payment made by the insurer?
A. 1315 B. 1325 C. 1335 D. 1345 E. 1355
7.A company pays an annual insurance premium of $1,000 at the beginning of the year to insure their
main assembly line. If they have to pay the premium each year until there is a failure on the line,
what is the expected total premium paid if the probability that the line is still working after t years is
e^(-t/2)?
A. $650 B. $930 C. $1540 D. $2000 E. $2540
8.The computer network for a company has two servers. If the failure times are independent and the
time until one server fails is uniformly distributed on [0; 20], and the other is uniformly distributed on
[0; 30], what is the variance of the time until at least one of the servers fails?
A. 16 B. 19 C. 22 D. 25 E. 28
9.When I am sick, I like to count the buses that pass my house. I have noticed that the number of buses
that pass can be modelled quite well by a Poisson random variable with mean 8 per hour from 8 until
10 am, and by a Poisson random variable with mean 5 per hour from 10 am until 2 pm. If exactly 5
buses drive past my house from 9:30-10:30 one morning, what is the probability that exactly 11 buses
drove past from 9 to 11?
A. 0.02 B. 0.16 C. 0.26 D. 0.38 E. 0.50