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

Miscellaneous 7 (II) · Q50

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

(iv) 20 white rats are available for an experiment. Twelve rats are male. Scientist randomly selects 5 rats number of female rats selected on a specific day.

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20 rats include 12 male, so 8 are female. Choosing 5 rats, the number of females selected is obtained by counting, so X is discrete. Since only 5 rats are chosen, X cannot exceed 5; and since 8 females are available (more than 5), X can reach all …

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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 $\in\{0,1,2\}$ .

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

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

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

…

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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: …

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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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