The probability distribution of a random variable $X$ is as follows: $p(x) = C(x^2 + x), \; x = -2, 1, 2$. Find the value of $C$. OR State the properties of Bernoulli trials. (Any two)

The probability distribution of a random variable X is as follows: p(x) = C(x² + x), x = -2, 1, 2. Find the va

Question 27 of 43

X

(OR)

State the properties of Bernoulli trials. (Any two)

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2023Subjective· 2mImportance★★★★★

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$\sum p(x)=2C+2C+6C=10C=1\Rightarrow C=0.1$ . OR: Bernoulli trials have two outcomes, are independent, with constant $p$ and a fixed number of trials.

Main part: $p(x)=C(x^2+x)$ for $x=-2,1,2$ . Evaluate each:

$p(-2)=C\big((-2)^2+(-2)\big)=C(4-2)=2C,$

$p(1)=C(1+1)=2C,\qquad p(2)=C(4+2)=6C.$

Since the probabilities must sum to $1$ :

$2C+2C+6C=10C=1\;\Rightarrow\;C=\frac{1}{10}=0.1.$

OR part — properties of Bernoulli trials (any two):

Each trial has exactly two mutually exclusive outcomes — success and failure.
The trials are independent of one another. …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set MARCH1 markMCQ
$Q. Which variable of the following will be an illustration of discrete variable?$
(a) Height of a student
(b) Weight of a student
(c) Blood pressure of a student
(d) Birth year of a student
›Reveal solutionSolution

Birth year takes countable whole-number values, so it is discrete.

A discrete variable assumes only isolated, countable values, whereas a continuous variable can take any value in an interval. Height, weight and blood pressure of a student are measured on a continuous scale, so they are continuous. The **birt …

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CBSE 2025Set MARCH1 markMCQ
$Q. Which variable of the following will be an illustration of continuous variable?$
(a) Number of accidents occurring at any place
(b) Number of rainy days during a year
(c) Maximum temperature during a day
(d) Number of children in a family
›Reveal solutionSolution
The maximum temperature during a day is a continuous variable, because it can take any value in an interval — option (c).

GSEB Class-12 Statistics, Random Variable chapter:

A discrete variable takes isolated (usually whole-number) values obtained by counting.

A continuous variable can take any value within a range and is obtained by measurement.

Checking the options:

Number of accidents — a count → discrete.

Number of rainy days — a count → discrete. …
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CBSE 2023Set MARCH1 mark
$Q. Define discrete random variable.$
›Reveal solutionSolution

A discrete random variable takes only countable (finite or countably infinite), isolated values.

A random variable is a real-valued function defined on the sample space of a random experiment. It is called a discrete random variable when the set of values it can assume is countable — either finite or countably infinite — and the values are distinct and separated (e.g. the number of heads in tosses of a coin, the number of defective items in a lot). Between two …

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CBSE 2022Set MARCH1 markMCQ
$Q. Which variable of the following will be an illustration of discrete variable?$
(a) Height of a student
(b) Weight of a student
(c) Blood pressure of a student
(d) Birth year of a student
›Reveal solutionSolution

Birth year takes only isolated whole-number values, so it is a discrete variable; height, weight and blood pressure are continuous.

Reasoning. A discrete variable can assume only specific separated values (usually counts), while a continuous variable can take any value in an interval. Height, weight and blood pressure can take any value on a …

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Q.The probability distribution of a random variable $X$ is as follows: $p(x) = C(x^2 + x), \; x = -2, 1, 2$ . Find the value of $C$ .

Concept understanding — Random Variable and Probability Mass Function

Q.The probability distribution of a random variable XXX is as follows: p(x)=C(x2+x), x=−2,1,2p(x) = C(x^2 + x), \; x = -2, 1, 2p(x)=C(x2+x),x=−2,1,2. Find the value of CCC.

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Q.The probability distribution of a random variable $X$ is as follows: $p(x) = C(x^2 + x), \; x = -2, 1, 2$ . Find the value of $C$ .

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