The discrete random variable X has the probability function | $X$ | $1$ | $2$ | $3$ | $4$ | | --- | --- | --- | --- | --- | | $P(X = x)$ | $k$ | $2k$ | $3k$ | $4k$ | Show that $k = 0.1$

The discrete random variable X has the probability – Class 12 Business Mathematics Statistics

Question 40 of 41

The discrete random variable X has the probability function

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

Show that $k = 0.1$

Puducherry TnboardTamil Nadu HSC (DGE) Commerce Board 2026Subjective· 2mImportance★★★★★

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For any probability mass function the total probability is $1$ . Summing $k+2k+3k+4k=10k$ and equating to $1$ gives $k=0.1$ .

In the Tamil Nadu HSC Business Mathematics syllabus, a discrete probability distribution is valid only when $\sum P(X=x)=1$ and every $P(X=x)\ge 0$ .

Step 1 — Add all the probabilities:

$P(X=1)+P(X=2)+P(X=3)+P(X=4)=k+2k+3k+4k=10k.$

Step 2 — Apply the total-probability condition: …