Identify the random variable as either discrete or continuous in each of the following. Write down the range o

Miscellaneous 7 (II) · Q47

Q. Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

(i) An economist is interested the number of unemployed graduate in the town of population 1 lakh.

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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✓ Free question

The number of unemployed graduates is obtained purely by counting people, and it cannot exceed the town's total population of 1 lakh. So X is discrete, with range $\{0,1,2,\ldots,100000\}$ .

✓Final answer

Discrete random variable; range = {0, 1, 2, ..., 1,00,000}.

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

CBSE 2024Set ANNUAL2 marks
$Q. If two coins are tossed simultaneously, write the probability distribution of the number of heads.$
›Reveal solutionSolution

Two-coin sample space $\{HH,HT,TH,TT\}$ ; $X=$ number of heads.

Sample space: $\{HH,HT,TH,TT\}$ , each with probability $\dfrac14$ . $X=$ number of heads $\in\{0,1,2\}$ .

$P(X=0)=P(TT)=\dfrac14$

$P(X=1)=P(HT)+P(TH)=\dfrac24=\dfrac12$

$P(X=2)=P(HH)=\dfrac14$

$X$ 0 1 2
$P(X)$ $1/4$ $1/2$ $1/4$

✓Final answer
$P(X=0)=\dfrac14,\ P(X=1)=\dfrac12,\ P(X=2)=\dfrac14$
CBSE 2016Set ANNUAL2 marks
$P(X \le 4)$
›Reveal solutionSolution

Find $k$ from $\sum P(X=x)=1$ , then sum the probabilities for $X=1,2,3,4$ .

$X=x$ 1 2 3 4 5
$P(X=x)$ $k$ $2k$ $3k$ $4k$ $5k$

Since total probability is 1:

$k+2k+3k+4k+5k=1 \Rightarrow 15k=1 \Rightarrow k=\frac{1}{15}$

$P(X\le4)=P(1)+P(2)+P(3)+P(4)=k+2k+3k+4k=10k=\frac{10}{15}=\frac23$

✓Final answer
$P(X\le4)=\dfrac23$

$X$	0	1	2
$P(X)$	$1/4$	$1/2$	$1/4$

X = x	1	2	3	4	5
P(X = x)	k	2k	3k	4k	5k

$X=x$	1	2	3	4	5
$P(X=x)$	$k$	$2k$	$3k$	$4k$	$5k$

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Q.Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

Concept understanding — Discrete Random Variable

Q.Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

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