Question

Which of the following statements are TRUE?

Note that there may be more than one correct answer; select all that are true.

There are countably infinite values of X in a continuous uniform distribution.

For a continuous uniform distribution defined on the interval [a,b], P(X < a) and P(X > b) is undefined.

The mean and the variance of a continuous uniform random variable are the same.

In a continuous uniform distribution, the mean and the median are the same.

In a continuous uniform distribution, the height of the curve, f(x), is the same for all values of the random variable X.

Answer 1

The first statement is true because the given distribution is continuous distribution so it having an interval there fore X takes an countably infinite values .

Now in second statement range is given [ a,b] so x takes values in this interval ...therefore P( x < a ) and P (x > b) is undefined because this values are not include in the given interval .Therefore this statement is also true .

Now in statement three mean of continuous uniform distribution is (a+b)/2 .

And variance is . There fore this two are not same ,so this is an false statement.

In the fourth statement mean of uniform distribution is (a+b)/2 and median is also (a+b)/2 . Therefore both are same .so given statement is true .

Now in fifth statement ..since uniform distribution is an rectangular type of distribution so the height of the curve f(x) is same for all values of rv x . So this statement is true .

Only third statement is false other all are true .