The random variable X has probability distribution PX of the following form- PX- k if X-0 2k if X-1 3k if X-2 0 otherwisea determine value of Kb Find PX- 2- PX- 2- PX- 2

(a) As Sum of all probabilities should be #160; #160; ⇒ k+2k+3k=1 ⇒ k=1/6 (b) P(x lt;2)=p(x=0)+p(x=1)=k+2k=3(16)=12 #160; p( ...

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Standard XII

Mathematics

Probability Distribution

The random va...

Question

The random variable $X$ has probability distribution $P (X)$ of the following form.
$P (X) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} k i f X = 0 2 k i f X = 1 3 k i f X = 2 0 o t h e r w i s e \end{matrix}$
(a) determine value of $K$
(b) Find $P (X < 2), P (X \leq 2), P (X \geq 2)$

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Solution

$(a)$ As Sum of all probabilities should be
$\Rightarrow k + 2 k + 3 k = 1 \Rightarrow k = 1 / 6$
$(b)$ $P (x < 2) = p (x = 0) + p (x = 1) = k + 2 k = 3 (\frac{1}{6}) = \frac{1}{2}$
$p (x \leq 2) = \frac{1}{2} + 3 k = \frac{1}{2} + \frac{3}{6} = \frac{1}{2} + \frac{1}{2} = 1$
$P (x \geq 2) = 3 k + 0 = 3 (\frac{1}{6}) + 0 = \frac{1}{2}$

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The random variable X has probability distribution P(X) of the following form.P(X)=⎧⎪ ⎪⎨⎪ ⎪⎩kifX=02kifX=13kifX=20otherwise(a) determine value of K(b) Find P(X<2),P(X≤2),P(X≥2)

(a) As Sum of all probabilities should be ⇒k+2k+3k=1⇒k=1/6(b) P(x<2)=p(x=0)+p(x=1)=k+2k=3(16)=12 p(x≤2)=12+3k=12+36=12+12=1 P(x≥2)=3k+0=3(16)+0=12

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$P (X) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} k i f X = 0 2 k i f X = 1 3 k i f X = 2 0 o t h e r w i s e \end{matrix}$
(a) determine value of $K$
(b) Find $P (X < 2), P (X \leq 2), P (X \geq 2)$