A random variable X has a density function . Find the variance of X.

Two discrete random variables X and Y have a joint probability function f(x,y) given in the following table: f(x,y) x=0 1 2 y=0 0.30 0.12 0.18 1 0.20 0.12 0.08 Find the mean of Y.

A prescription drug firm wants to know the effectiveness of a new drug in animal test, that is, percentage (p) of diseased animals cured after the use of the drug. So, the form has to run some tests.  The firm uses the sample proportion to estimate p and wishes that the maximum error is less than 3% with 95% confidence. Find the minimal number of tests that are required to run.  

A prescription drug firm wants to know the effectiveness of a new drug in animal test, that is, percentage (p) of diseased animals cured after the use of the drug. So the form has to run some tests.  Suppose that the firm arranges 50 tests and it turns out that 24 animals are cured after the use of the drug. Give a point estimate for p.  

The following observations are the numbers of calls received by an office in ten working days.                4 , 4,  2,  3,  8,  9,  3,  4,  3,  4 Find the mode(s).  

A random sample of size 10 is as follows:             2.3,  4.3, 12.6,  4.2,  1.0,  4.5,  4.1,  8.5,  4.0,  4.8                               Find the sample mean.

The following observations are the numbers of calls received by an office in ten working days.                4 , 4,  2,  3,  8,  9,  3,  5,  3,  4 Find the third quartile.

A random sample of size 10 is as follows:         0.5,  1.8,   0.2,    0.5,   0.0,   1.0,   1.3,   2.3,   0.2,   0.8 Find all the mode(s).

The following observations are the numbers of calls received by an office in ten working days.                4 , 4,  2,  3,  8,  10,  3,  5,  3,  4 Find the 10% trimmed mean.

Determine whether the following statement is true:          The cumulative distribution function of an exponential random variable with  mean 2  is given by