(C) We know that the sum of all probabilities in a distribution must be equal to $1$.$\sum P(X = x) = 0 + k + 2k + 2k + 3k + k^2 + 2k^2 + 7k^2 + k = 1

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(C) We know that the sum of all probabilities in a distribution must be equal to $1$.$\sum P(X = x) = 0 + k + 2k + 2k + 3k + k^2 + 2k^2 + 7k^2 + k = 1$$10k^2 + 9k - 1 = 0$$(10k - 1)(k + 1) = 0$Since $k$ must be positive for probabilities to be valid, we have $k = \frac{1}{10}$.We need to find $P(0 $P(0 Substituting $k = \frac{1}{10}$, we get $P(0 < X < 4) = 5 \times \frac{1}{10} = \frac{1}{2}$.

Class 12 Mathematics Probability Probability distribution

Medium

The probability distribution of a random variable $X$ is given below:
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X = x)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$

Then, $P(0 < X < 4)$ is equal to:

TS EAMCET 2021 All TS EAMCET

A
$\frac{4}{5}$
B
$\frac{3}{5}$
C
$\frac{1}{2}$
D
$\frac{1}{4}$

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$A$ typist claims that he prepares a typed page with typo errors of $1$ per $10$ pages. In a typing assignment of $40$ pages, if the probability that the typo errors are at most $2$ is $p$, then $e^2 p=$

MediumTS EAMCET 2025

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The probability distribution of a discrete random variable $X$ is given by the following table:
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$P(X = x)$ $k$ $2k$ $4k$ $2k$ $k$

Then the value of $P(X \leq 2)$ is:

MediumMHT CET 2020

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EasyMHT CET 2010

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$A$ random variable $X$ has the following probability distribution. For events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,what is the probability $P(E \cup F)$?

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

Medium

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If a random variable $X$ denotes the number that appears on the upper face of a die when it is rolled,then $\frac{\text{Variance of } X}{\text{Mean of } X}$ is equal to

EasyTS EAMCET 2021

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$X = x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X = x)$	$0$	$k$	$2k$	$2k$	$3k$	$k^2$	$2k^2$	$7k^2 + k$

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

The probability distribution of a random variable $X$ is given below:$X = x$$0$$1$$2$$3$$4$$5$$6$$7$$P(X = x)$$0$$k$$2k$$2k$$3k$$k^2$$2k^2$$7k^2 + k$Then, $P(0 < X < 4)$ is equal to:

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$A$ typist claims that he prepares a typed page with typo errors of $1$ per $10$ pages. In a typing assignment of $40$ pages, if the probability that the typo errors are at most $2$ is $p$, then $e^2 p=$

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The probability distribution of a random variable $X$ is given below:
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X = x)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$

Then, $P(0 < X < 4)$ is equal to:

The probability distribution of a discrete random variable $X$ is given by the following table:
$X = x$ $0$ $1$ $2$ $3$ $4$
$P(X = x)$ $k$ $2k$ $4k$ $2k$ $k$

Then the value of $P(X \leq 2)$ is:

$A$ random variable $X$ has the following probability distribution. For events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,what is the probability $P(E \cup F)$?

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$