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.
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\n\\\\\\Rightarrow 4k=0.4\n\\\\\\Rightarrow k=\\dfrac{0.4}4\n\\\\\\Rightarrow k=0.1"
Thus, probability distribution is:
"x=-2, f(x)=0.1\n\\\\x=-1, f(x)=0.1\n\\\\x=0,f(x)=0.2\n\\\\x=1,f(x)=0.2\n\\\\x=2,f(x)=0.3\n\\\\x=3,f(x)=0.1"
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