The random variable X has a probability distribution P(X) of the following form, where k is some number : ![\left \{ {{k,\ if\ x=0} \atop {2k,\ if\ x=1 \atop{3k,\ if\ x=2 \atop {0,otherwise} \right \](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bk%2C%5C+if%5C+x%3D0%7D+%5Catop+%7B2k%2C%5C+if%5C+x%3D1+%5Catop%7B3k%2C%5C+if%5C+x%3D2+%5Catop+%7B0%2Cotherwise%7D+%5Cright++%5C+ "\left \{ {{k,\ if\ x=0} \atop {2k,\ if\ x=1 \atop{3k,\ if\ x=2 \atop {0,otherwise} \right \")
(a) Determine the value of k.
(b) Find P (X < 2), P (X ≤ 2), P(X ≥ 2).
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here k=0
P(x<2) =0 because if x<2 x has infinite values and value of 3/y such that y->infinity=0 so P(x<2)=0similarly p(x_<2),p(x>_2)=0
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