Question

A random variable X has the following probability function : x: -2 -1 0 1 2 3 f(x): 0*1 k 0*1 2 2k 0*3 3k (i) Determine the distribution function F(x) of X.

Answer 1

Solution:

The sum of probabilities in a probability distribution is 1.

So, $0.1+k+0.2+2k+0.3+k=1$

$\Rightarrow 4k+0.6=1 \\\Rightarrow 4k=0.4 \\\Rightarrow k=\dfrac{0.4}4 \\\Rightarrow k=0.1$

Thus, probability distribution is:

$x=-2, f(x)=0.1 \\x=-1, f(x)=0.1 \\x=0,f(x)=0.2 \\x=1,f(x)=0.2 \\x=2,f(x)=0.3 \\x=3,f(x)=0.1$