(B) For a probability distribution,the sum of all probabilities must be equal to $1$.Therefore,$\sum P(X) = 1$.$K + \frac{1}{6} + \frac{3}{8} + 2K + \

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(B) For a probability distribution,the sum of all probabilities must be equal to $1$.Therefore,$\sum P(X) = 1$.$K + \frac{1}{6} + \frac{3}{8} + 2K + \frac{1}{12} = 1$Combine the terms with $K$ and the constant fractions:$3K + (\frac{1}{6} + \frac{3}{8} + \frac{1}{12}) = 1$Find a common denominator for the fractions,which is $24$:$3K + (\frac{4}{24} + \frac{9}{24} + \frac{2}{24}) = 1$$3K + \frac{15}{24} = 1$$3K + \frac{5}{8} = 1$$3K = 1 - \frac{5}{8}$$3K = \frac{3}{8}$$K = \frac{1}{8}$

Class 12 Mathematics Probability Probability distribution

Easy

The random variable $X$ has the following probability distribution:
| $X$ | $8$ | $12$ | $16$ | $20$ | $24$ |
|---|---|---|---|---|---|
| $P(X)$ | $K$ | $\frac{1}{6}$ | $\frac{3}{8}$ | $2K$ | $\frac{1}{12}$ |
Then the value of $K$ is:

MHT CET 2022 All MHT CET

A
$\frac{1}{4}$
B
$\frac{1}{8}$
C
$\frac{3}{2}$
D
$\frac{1}{2}$

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For the probability distribution given by

$x = x_{i}$ $0$ $1$ $2$

$P_{i}$ $\frac{25}{36}$ $\frac{5}{18}$ $\frac{1}{36}$

the standard deviation $(\sigma)$ is

MediumKCET 2018

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Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.

Difficult

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$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ is

DifficultTS EAMCET 2004

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For the following probability distribution,find the $Var(X)$.
$X$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X)$ $0.1$ $0.2$ $0.2$ $0.3$ $0.15$ $0.05$

(Given : $(0.25)^2 = 0.0625$,$(0.35)^2 = 0.1225$,$(0.45)^2 = 0.2025$)

MediumMHT CET 2024

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If the range of a random variable $X$ is $\{0, 1, 2, 3, 4, \ldots\}$ with $P(X=k) = \frac{(k+1)a}{3^k}$ for $k \geq 0$,then $a$ is equal to

DifficultAP EAMCET 2005

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$x = x_{i}$	$0$	$1$	$2$
$P_{i}$	$\frac{25}{36}$	$\frac{5}{18}$	$\frac{1}{36}$

$X$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X)$	$0.1$	$0.2$	$0.2$	$0.3$	$0.15$	$0.05$

The random variable $X$ has the following probability distribution:| $X$ | $8$ | $12$ | $16$ | $20$ | $24$ ||---|---|---|---|---|---|| $P(X)$ | $K$ | $\frac{1}{6}$ | $\frac{3}{8}$ | $2K$ | $\frac{1}{12}$ |Then the value of $K$ is:

Similar Questions

For the probability distribution given by $x = x_{i}$ $0$ $1$ $2$ $P_{i}$ $\frac{25}{36}$ $\frac{5}{18}$ $\frac{1}{36}$ the standard deviation $(\sigma)$ is

Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.

$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ is

For the following probability distribution,find the $Var(X)$.$X$$-2$$-1$$0$$1$$2$$3$$P(X)$$0.1$$0.2$$0.2$$0.3$$0.15$$0.05$(Given : $(0.25)^2 = 0.0625$,$(0.35)^2 = 0.1225$,$(0.45)^2 = 0.2025$)

If the range of a random variable $X$ is $\{0, 1, 2, 3, 4, \ldots\}$ with $P(X=k) = \frac{(k+1)a}{3^k}$ for $k \geq 0$,then $a$ is equal to

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The random variable $X$ has the following probability distribution:
| $X$ | $8$ | $12$ | $16$ | $20$ | $24$ |
|---|---|---|---|---|---|
| $P(X)$ | $K$ | $\frac{1}{6}$ | $\frac{3}{8}$ | $2K$ | $\frac{1}{12}$ |
Then the value of $K$ is:

For the probability distribution given by

$x = x_{i}$ $0$ $1$ $2$

$P_{i}$ $\frac{25}{36}$ $\frac{5}{18}$ $\frac{1}{36}$

the standard deviation $(\sigma)$ is

For the following probability distribution,find the $Var(X)$.
$X$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X)$ $0.1$ $0.2$ $0.2$ $0.3$ $0.15$ $0.05$

(Given : $(0.25)^2 = 0.0625$,$(0.35)^2 = 0.1225$,$(0.45)^2 = 0.2025$)