Match P binomial,Q Poisson,R normal,S exponential to these probability laws. (1) f(x)=e-(x-)2/(22)/(2); (2) f(x)= nx px(1-p)n-x for x=0,…,n; (3) f(x)=e-x/x! for nonnegative integer x; (4) f(x)= e- x for x>0.

GATE 2026 MN – Question 15

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

Match P binomial,Q Poisson,R normal,S exponential to these probability laws. (1) $f(x)=e^{-(x-\mu)^2/(2\sigma^2)}/(\sigma\sqrt{2\pi})$; (2) $f(x)=\binom nx p^x(1-p)^{n-x}$ for x=0,…,n; (3) $f(x)=e^{-\mu}\mu^x/x!$ for nonnegative integer x; (4) $f(x)=\lambda e^{-\lambda x}$ for x>0.

P–2,Q–3,R–1,S–4
P–1,Q–3,R–2,S–4
P–3,Q–2,R–1,S–4
P–2,Q–4,R–3,S–1

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Correct answer: (A) P–2,Q–3,R–1,S–4

Explanation

The binomial counts successes in n trials and uses the binomial coefficient(2). Poisson mass uses the exponential and factorial expression(3). The symmetric Gaussian density is(1), and the positive waiting-time density is exponential(4). Therefore P–2,Q–3,R–1,S–4, A.

GATE 2026 MN – Question 15

Explanation

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