The random variable X has a probability distribution PX of the following form- where -k- is some number-PX-k- if x - 0 2k- if x - 13k- if x - 20- otherwiseDetermine the value of k-

Since, X has a probability distribution ∑ P(X)=1 According to the values given in the question, ∑ P(X) = P(X=0)+P(X=1)+P(X=2)+P(X2) ⇒ 1 = k+2k+3k+0 ⇒ 6k = 1 ⇒ ...

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Standard XII

Mathematics

Total Probability Theorem

The random va...

Question

The random variable $X$ has a probability distribution $P (X)$ of the following form, where ' $k$ ' is some number.
$P (X) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} k, & if x = 0 2 k, & if x = 1 3 k, & if x = 2 0, & otherwise \end{matrix}$

Determine the value of $k$ .

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Solution

Since, $X$ has a probability distribution
$\sum P (X) = 1$
According to the values given in the question,
$\sum P (X) = P (X = 0) + P (X = 1) + P (X = 2) + P (X > 2) \Rightarrow 1 = k + 2 k + 3 k + 0 \Rightarrow 6 k = 1 \Rightarrow k = \frac{1}{6}$

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Q. The random variable

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P (X) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} k, & if x = 0 2 k, & if x = 1 3 k, & if x = 2 0, & otherwise \end{matrix}

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Q. The random variable

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P (X) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} k, & x = 0 2 k, & x = 1 3 k, & x = 2 0, & otherwise \end{matrix}

then value of

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The random variable X has a probability distribution P(X) of the following form, where k is some number
$⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} K, i f X = 0 2 k, i f X = 1 3 k, i f X = 2 0, i f o t h e r w i s e \end{matrix}$

Determine the value of k

$⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} K, i f X = 0 2 k, i f X = 1 3 k, i f X = 2 0, i f o t h e r w i s e \end{matrix}$

Q. The random variable x has a probability distribution

P (x)

of the following form where

k

is some number:

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}

Determine the value of

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P (X \leq 2) .

Find $P (X < 2), P (X \leq 2), P (X \geq 2)$

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The random variable X has a probability distribution P(X) of the following form, where 'k' is some number. P(X)=⎧⎪ ⎪⎨⎪ ⎪⎩k, if x = 02k, if x = 13k, if x = 20, otherwise Determine the value of k.

Since, X has a probability distribution ∑P(X)=1 According to the values given in the question, ∑P(X) = P(X=0)+P(X=1)+P(X=2)+P(X>2)⇒1 = k+2k+3k+0⇒6k = 1⇒k = 16

The random variable $X$ has a probability distribution $P (X)$ of the following form, where ' $k$ ' is some number.
$P (X) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} k, & if x = 0 2 k, & if x = 1 3 k, & if x = 2 0, & otherwise \end{matrix}$

Determine the value of $k$ .

Since, $X$ has a probability distribution
$\sum P (X) = 1$
According to the values given in the question,
$\sum P (X) = P (X = 0) + P (X = 1) + P (X = 2) + P (X > 2) \Rightarrow 1 = k + 2 k + 3 k + 0 \Rightarrow 6 k = 1 \Rightarrow k = \frac{1}{6}$