Continuous Random Variables
Exercises for students:
Solve the following problems on paper and check your working using the above applet:
The continuous random variable X has probability density function f given by
| kx, | if 0 < x < 3, |
| f(x) = | k(6 - x), | if 3 < x < 6 |
| 0, | otherwise. |
where k is a constant.
(a) Find the value of k.
(b) Find the expectation and variance of X.
(c) Find the cumulative distribution function of X.
The continuous random variable X has probability density function f given by
| f(x) = | k(2 - x), | for 0 < x < 2 |
| 0, | otherwise. |
where k is a constant.
(a) Find the value of k.
(b) Find the expectation and variance of X.
(c) Find the cumulative distribution function of X.
(d) Find the median of X.
The random variable X has probability density function f given by:
| f(x) = | kx, | for 0 < x < 1 |
| 0, | otherwise. |
where k is a constant.
(a) Find the value of k.
(b) Find the expectation and variance of X.
(c) Find the cumulative distribution function of X.
(d) Find the median of X.
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