The random variable X has a probability distribution P X of the following form- where k is some numberK- if - X -0 l2 k - - if - X -13 k - - if - X -2 0- if otherwiselend matrix right- Find P X -2- P X - 2- P X - 2

Given distribution of X is [ X amp;0 amp;1 amp;2 amp;otherwise; P(X) amp;k amp; 2k amp; 3k ...

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Standard XII

Mathematics

Probability Distribution

The random va...

Question

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

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

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Solution

Given distribution of X is

$\begin{matrix} X & 0 & 1 & 2 & o t h e r w i s e P (X) & k & 2 k & 3 k & 0 \end{matrix}$

$P (X < 2) = P (0) + P (1) = k + 2 k = 3 k = 3 \times \frac{1}{6} = \frac{1}{2}$

$P (X \leq 2) = P (0) + P (1) + P (2) = k + 2 k + 3 k = 6 k = 6 \times \frac{1}{6} = 1$

and $P (X \geq 2) = P (2) + P (o t h e r w i s e) = 3 k + 0 = 3 \times \frac{1}{6} = \frac{1}{2}$

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Similar questions

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) = {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}

(a) Determine the value of

k

(b) Find

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

Q. The random variable X has probability distribution P(X) of the following form, where k is some number: (a) Determine the value of k . (b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).

Q. The random variable

X

has a probability distribution

P (X)

of the following form,

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

then value of

k

is:

Q. 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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The random variable X has a probability distribution P(X) of the following form, where k is some number ⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩K, if X=02k, if X=13k, if X=20, if otherwise Find P(X<2),P(X≤2),P(X≥2)

Given distribution of X is X 0 1 2otherwiseP(X)k 2k 3k 0​​​ P(X<2)=P(0)+P(1)=k+2k=3k=3×16=12 P(X≤2)=P(0)+P(1)+P(2)=k+2k+3k=6k=6×16=1 and P(X≥2)=P(2)+P(otherwise)=3k+0=3×16=12

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

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