SSC CGL Statistics – Random Variables & Probability Distributions – Level 3 · Challenge
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Mean = variance is the Poisson property; for the binomial, variance = mean × q < mean.
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SSC CGL Statistics – Random Variables & Probability Distributions – Level 3 · Challenge – 8 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
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1.
The mode of a binomial distribution with n = 15 and p = 0.4 is:
Correct Answer: A [6]
Explanation:
(n + 1)p = 6.4, not a whole number → mode = 6.
2.
In a normal distribution 30.85% of the items are below 40 and 6.68% are above 70. The mean and SD are:
Correct Answer: C [Mean 47.5, SD 15]
Explanation:
z = −0.5 and z = 1.5: 40 = μ − 0.5σ and 70 = μ + 1.5σ → 2σ = 30 → σ = 15, μ = 47.5.
3.
Statement-basedFor an exponential distribution with parameter λ, which of these is/are true?
I. Mean = SD = 1/λ
II. P(X > s + t | X > s) = P(X > t)
III. The median is greater than the mean
I. Mean = SD = 1/λ
II. P(X > s + t | X > s) = P(X > t)
III. The median is greater than the mean
Correct Answer: B [Only I and II]
Explanation:
Median = 0.6931/λ < 1/λ = mean, so III is false.
4.
Nothing is known about the shape of a distribution except mean 60 and SD 8. By Chebyshev's inequality, the proportion of values between 44 and 76 is:
Correct Answer: A [At least 75%]
Explanation:
44 and 76 are μ ± 2σ → at least 1 − 1/2² = 3/4 (95.45% needs a normal shape; 88.89% is for k = 3).
5.
X ~ Poisson(1.5) and Y ~ Poisson(2.5) are independent. P(X + Y = 1) is:
Correct Answer: D [0.0733]
Explanation:
X + Y ~ Poisson(4): P(1) = 4e⁻⁴ ≈ 0.0733.
6.
For a normal distribution with SD 12, the quartile deviation is approximately:
Correct Answer: B [8.09]
Explanation:
QD = 0.6745σ = 0.6745 × 12 ≈ 8.09 (9.57 is the mean deviation 0.7979σ).
7.
Reverse questionY = 4 − 3X with E(Y) = −8 and Var(Y) = 18. Then E(X) and Var(X) are:
Correct Answer: C [4 and 2]
Explanation:
−8 = 4 − 3E(X) → E(X) = 4; 18 = 9Var(X) → Var(X) = 2.
8.
Odd one outWhich is NOT a property of the binomial distribution?
Correct Answer: D [Mean = variance for every n and p]
Explanation:
Mean = variance is the Poisson property; for the binomial, variance = mean × q < mean.
➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics
📘 SSC CGL 2026 – Statistics (Tier II Paper II)
Here you get the answer with a one-line explanation. 657 original questions with worked answers · notes, formulas, figures and statistical tables (z, t, χ², F) · practice sets + 3 mock tests
Get the book – ₹149 More quizzes
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