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A random variable X has a density function . Find the expectation  E(X2). 

A rare disease occurs with probability 0.002 in a large population.  Now we select 1000 people at random.  Find the probability that at most 3 people have contracted the disease.  

Extensive experience with fans of certain type used in diesel engines has suggested that the exponential distribution provides a good model for time until failure. Suppose the mean time until failure is 20,000 hours. What is the probability that a randomly selected fan has a lifetime less than 10,000 hours?

A randomly selected computer chip from a product line is defective with probability of 0.005.  Find the probability that 4 or 5 chips are defective among a random sample of 1000 chips.   

A box contains 2000 red beans and 3000 green beans. Pick up 10 beans at random without replacement. Use X to denote the number of the red beans obtained. What is the distribution of X?

X and Y are two independent random variables having Poisson distributions with means E(X)=3 and E(Y)=5, respectively Find the variance of X+Y.

Adult females have forearm lengths that are normally distributed with mean 17.75 in. and standard deviation 0.65 in. Find the upper quartile length of a female’s forearm – that is, a length x that is exceeded by 25% of adult females.

Suppose 64 observations are sampled from a normal population with mean 5 and standard deviation 4. Let  

Suppose we have 20 observations from a normal population with mean  10 and variance 3. Let  

Suppose we have 20 observations from a normal population with mean 10 and standard deviation 3. Let