SSC CGL Statistics – Random Variables & Probability Distributions – Level 1 · Warm-up

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SSC CGL Statistics – Random Variables & Probability Distributions – Level 1 · Warm-up – 12 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.  
A random variable X has P(X = x) = x/15 for x = 1, 2, 3, 4, 5. What is P(X ≥ 4)?

Correct Answer: C [3/5]

Explanation:

P(4) + P(5) = 4/15 + 5/15 = 9/15 = 3/5.

2.  
P(X = x) = c(x + 1) for x = 0, 1, 2, 3 is a probability mass function. The value of c is:

Correct Answer: A [1/10]

Explanation:

Total = c(1 + 2 + 3 + 4) = 10c = 1 → c = 1/10.

3.  
If E(X) = 4, then E(3X + 5) equals:

Correct Answer: B [17]

Explanation:

E(aX + b) = aE(X) + b = 12 + 5 = 17.

4.  
If Var(X) = 9, the standard deviation of (5 − 2X) is:

Correct Answer: D [6]

Explanation:

SD(aX + b) = |a| × SD = 2 × 3 = 6; the constant 5 does not matter.

5.  
For a binomial distribution with n = 20 and p = 0.3, the mean and variance are:

Correct Answer: C [Mean 6, variance 4.2]

Explanation:

Mean = np = 6; variance = npq = 6 × 0.7 = 4.2.

6.  
A fair coin is tossed 4 times. The probability of exactly 2 heads is:

Correct Answer: B [3/8]

Explanation:

Answer: 3/8. ⁴C₂ (1/2)⁴ = 6/16 = 3/8.

7.  
A Poisson variable has variance 4. Its standard deviation is:

Correct Answer: D [2]

Explanation:

Poisson: variance = mean = m = 4 → SD = √4 = 2.

8.  
Statement-basedFor a normal distribution, which is/are correct?
I. Mean = median = mode
II. β₂ = 3 (mesokurtic)

Correct Answer: A [Both I and II]

Explanation:

The normal curve is symmetric (I) and its kurtosis β₂ is exactly 3 (II).

9.  
For a normal distribution, the area lying within μ ± 2σ is about:

Correct Answer: D [95.45%]

Explanation:

Φ(2) − Φ(−2) = 2 × 0.9772 − 1 = 0.9545.

10.  
An exponential distribution has parameter λ = 0.25. Its mean is:

Correct Answer: C [4]

Explanation:

Answer: 4. Mean = 1/λ = 1/0.25 = 4.

11.  
Fill in the blankFor a binomial distribution with 0 < p < 1, the variance is always ______ the mean.

Correct Answer: B [less than]

Explanation:

Variance/mean = q and 0 < q < 1, so npq < np.

12.  
Match the followingMatch each distribution with its mean:
P. Binomial (n, p) Q. Poisson (m) R. Exponential (λ)
1. m 2. 1/λ 3. np

Correct Answer: A [P-3, Q-1, R-2]

Explanation:

Binomial np; Poisson m; exponential 1/λ.

➤ 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)
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