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Assume A and B are two events with P(A)=0.41 and P(B)=0.60. Which of the following statements is always true? A.   

Assume α=8, β=λ=2. The lifetime (X, in months) of a light bulb has a gamma distribution with α and β=λ.  Find the probability that the lifetime is between 10 and 14 months.

An engineer has 20 red marbles and 30 purple marbles. He mixes them, randomly put them in two boxes with equal numbers of marbles.  Now he randomly selects a box and takes out two marbles without replacement.  What is the probability of getting one red marble?

A random sample of size 64 is from an exponential distribution with parameter =1.2.  See page 195 for the definition of the exponential distribution.    Let 

A high school student flips a fair coin 20 times and obtains 10 heads. What is the probability that there is 1 head in his first two flips?      

The following observations are the numbers of customers in a service center in ten days.                9, 9, 8, 13, 19, 5, 11, 12, 10, 8 Find the 10% trimmed mean.

In a small island, earthquakes occur twice per year on average. Assume the number of the earthquakes follows from a Poisson distribution. What is the probability that there are 3 to 6 earthquakes from January 1,  2029 to  December 31, 2030?

Assume α=3, β=λ=2.  The lifetime (in years) for a certain type of batteries has a gamma distribution with  α and  β.  Randomly select 100 batteries. What is the expected number of batteries whose lifetimes are at most  λ years?

A normal population has a standard deviation

A candidate for public office is thought to have support of 60% of the voters. Randomly select 100 voters.  Use normal approximation to find the probability for the event that between 50 and 60 (exclusive) voters will support the candidate.