A random variable X has pdf:
X
1
2
3
f(x)
1/8
3/8
3/8
1/8
a)
"F(0)=P(X\\leq 0)=P(X=0)""=\\dfrac{1}{8}"
"F(1)=P(X\\leq 1)=P(X=0)+P(X=1)"
"=\\dfrac{1}{8}+\\dfrac{3}{8}=\\dfrac{1}{2}"
"F(2)=P(X\\leq2)=P(X=0)+P(X=1)+P(X=2)"
"=\\dfrac{1}{8}+\\dfrac{3}{8}+\\dfrac{3}{8}=\\dfrac{7}{8}"
"F(1)=P(X\\leq 3)=P(X=0)+P(X=1)"
"+P(X=2)+P(X=3)=\\dfrac{1}{8}+\\dfrac{3}{8}+\\dfrac{3}{8}+\\dfrac{1}{8}=1"
"F(x) = \\begin{cases}\n 0 &x<0 \\\\\n 1\/8 & 0\\leq x<1\\\\\n 1\/2 & 1\\leq x<2\\\\\n 7\/8 & 2\\leq x<3\\\\\n 1 & x\\geq 3\\\\\n\\end{cases}"
b)
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