(A) For a probability distribution,the sum of all probabilities must be equal to $1$.$\sum P(x) = k + 0.3 + 0.15 + 0.15 + 0.1 + 2k = 1$$3k + 0.7 = 1$$

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(A) For a probability distribution,the sum of all probabilities must be equal to $1$.$\sum P(x) = k + 0.3 + 0.15 + 0.15 + 0.1 + 2k = 1$$3k + 0.7 = 1$$3k = 0.3$$k = 0.1$Now,the expected value $E(x)$ is calculated as $\sum x_i P(x_i)$:$E(x) = (0 \times k) + (1 \times 0.3) + (2 \times 0.15) + (3 \times 0.15) + (4 \times 0.1) + (5 \times 2k)$Substitute $k = 0.1$:$E(x) = (0 \times 0.1) + (1 \times 0.3) + (2 \times 0.15) + (3 \times 0.15) + (4 \times 0.1) + (5 \times 0.2)$$E(x) = 0 + 0.3 + 0.3 + 0.45 + 0.4 + 1.0$$E(x) = 2.45$

Class 12 Mathematics Probability Probability distribution

Easy

The following table shows the probability distribution of smart phones sold in a shop per day:
Number of smart phones $(x)$ $0$ $1$ $2$ $3$ $4$ $5$
Probability $(P(x))$ $k$ $0.3$ $0.15$ $0.15$ $0.1$ $2k$

Then $E(x) = ?$

Number of smart phones $(x)$	$0$	$1$	$2$	$3$	$4$	$5$
Probability $(P(x))$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

MHT CET 2022 All MHT CET

A
$2.45$
B
$2.55$
C
$0.55$
D
$0.75$

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Probability

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Probability distribution

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If a random variable $X$ has the following probability distribution, then its variance is
$X=x$ $1$ $3$ $5$ $2$
$P(X=x)$ $3 K^2$ $K$ $K^2$ $2 K$

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Find the variance of the number obtained on a throw of a fair die.

Medium

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The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:
$X$ $-3$ $-1$ $0$ $1$ $3$ $5$ $7$ $9$
$F(X)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,find $P[X=3]$.

$X$	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F(X)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

EasyMHT CET 2020

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Let a sample space be $S = \{\omega_{1}, \omega_{2}, \dots, \omega_{6}\}$. Which of the following assignments of probabilities to each outcome is valid?
Outcome $\omega_1$ $\omega_2$ $\omega_3$ $\omega_4$ $\omega_5$ $\omega_6$
$(e)$ $0.1$ $0.2$ $0.3$ $0.4$ $0.5$ $0.6$

Easy

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$A$ manufacturing company noticed that $1 \%$ of its products are defective. If a dealer orders for $300$ items from this company,then the probability that the number of defective items is at most one is

MediumAP EAMCET 2024

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Outcome	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$
$(e)$	$0.1$	$0.2$	$0.3$	$0.4$	$0.5$	$0.6$

The following table shows the probability distribution of smart phones sold in a shop per day:Number of smart phones $(x)$$0$$1$$2$$3$$4$$5$Probability $(P(x))$$k$$0.3$$0.15$$0.15$$0.1$$2k$Then $E(x) = ?$

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If a random variable $X$ has the following probability distribution, then its variance is $X=x$$1$$3$$5$$2$$P(X=x)$$3 K^2$$K$$K^2$$2 K$

Find the variance of the number obtained on a throw of a fair die.

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:$X$$-3$$-1$$0$$1$$3$$5$$7$$9$$F(X)$$0.1$$0.3$$0.5$$0.65$$0.75$$0.85$$0.90$$1$Then,find $P[X=3]$.

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The following table shows the probability distribution of smart phones sold in a shop per day:
Number of smart phones $(x)$ $0$ $1$ $2$ $3$ $4$ $5$
Probability $(P(x))$ $k$ $0.3$ $0.15$ $0.15$ $0.1$ $2k$

Then $E(x) = ?$

If a random variable $X$ has the following probability distribution, then its variance is
$X=x$ $1$ $3$ $5$ $2$
$P(X=x)$ $3 K^2$ $K$ $K^2$ $2 K$

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:
$X$ $-3$ $-1$ $0$ $1$ $3$ $5$ $7$ $9$
$F(X)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,find $P[X=3]$.

Let a sample space be $S = \{\omega_{1}, \omega_{2}, \dots, \omega_{6}\}$. Which of the following assignments of probabilities to each outcome is valid?
Outcome $\omega_1$ $\omega_2$ $\omega_3$ $\omega_4$ $\omega_5$ $\omega_6$
$(e)$ $0.1$ $0.2$ $0.3$ $0.4$ $0.5$ $0.6$