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

$$0.1+k+0.12+2k+0.3+3k=1$$

$$6k=0.48$$

$$k=0.08$$

$$F_X(x) = \begin{cases} 0 & x<-2 \\ 0.1 &-2\leq x<-1\\ 0.18 &-1\leq x<0\\ 0.3 &0\leq x<1\\ 0.46 &1\leq x<2\\ 0.7 &2\leq x<3\\ 1 &x\geq 3\\ \end{cases}$$