Mean and Variance Probability MCQs
Mean and Variance Probability MCQs
Class: CBSE Class 12 Mathematics
Section: Probability
Topic: Mean and Variance of Probability Distributions
Exam Focus: CBSE Board Examinations
Section: Probability
Topic: Mean and Variance of Probability Distributions
Exam Focus: CBSE Board Examinations
Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination standard practice. Each question includes a detailed explanation for concept clarity.
Q1. The mean of a binomial distribution B(n, p) is:
Answer: B) np
Mean of binomial distribution = np. It represents the expected number of successes in n trials.
Mean of binomial distribution = np. It represents the expected number of successes in n trials.
Q2. Variance of binomial distribution is:
Answer: C) npq
Variance measures spread. For binomial distribution, Variance = npq where q = 1 − p.
Variance measures spread. For binomial distribution, Variance = npq where q = 1 − p.
Q3. If mean = 5 and n = 10, then p equals:
Answer: A) 0.5
Mean = np ⇒ 5 = 10p ⇒ p = 0.5.
Mean = np ⇒ 5 = 10p ⇒ p = 0.5.
Q4. Standard deviation of binomial distribution is:
Answer: B) √npq
Standard deviation is square root of variance.
Standard deviation is square root of variance.
Q5. If p = 0.3, q equals:
Answer: B) 0.7
q = 1 − p = 1 − 0.3 = 0.7.
q = 1 − p = 1 − 0.3 = 0.7.
Q6. If variance = 6 and np = 10, then q equals:
Answer: A) 0.6
Variance = npq ⇒ 6 = 10q ⇒ q = 0.6.
Variance = npq ⇒ 6 = 10q ⇒ q = 0.6.
Q7. Mean of probability distribution is also called:
Answer: C) Expectation
Mean represents expected value of random variable.
Mean represents expected value of random variable.
Q8. If X has mean 4, then E(X) equals:
Answer: B) 4
E(X) denotes expectation which equals mean.
E(X) denotes expectation which equals mean.
Q9. Variance is always:
Answer: B) Positive
Variance is square of deviation, hence non‑negative.
Variance is square of deviation, hence non‑negative.
Q10. If p = 1, variance becomes:
Answer: C) 0
If p = 1, q = 0 ⇒ Variance = npq = 0.
If p = 1, q = 0 ⇒ Variance = npq = 0.
Q11. If n = 8, p = 0.5, mean equals:
Answer: B) 4
Mean = np = 8 × 0.5 = 4.
Mean = np = 8 × 0.5 = 4.
Q12. Variance for above data equals:
Answer: B) 2
Variance = npq = 8 × 0.5 × 0.5 = 2.
Variance = npq = 8 × 0.5 × 0.5 = 2.
Q13. If mean = variance in binomial distribution, then p equals:
Answer: B) 1
np = npq ⇒ q = 1 ⇒ p = 0 or 1. Valid case → p = 1.
np = npq ⇒ q = 1 ⇒ p = 0 or 1. Valid case → p = 1.
Q14. Expectation of constant k equals:
Answer: B) k
E(k) = k since constant has no variability.
E(k) = k since constant has no variability.
Q15. Variance of constant equals:
Answer: C) 0
No deviation from mean ⇒ variance 0.
No deviation from mean ⇒ variance 0.
Q16. If SD = 3, variance equals:
Answer: C) 9
Variance = (SD)² = 9.
Variance = (SD)² = 9.
Q17. If variance = 0, distribution is:
Answer: B) Constant
No spread means all values identical.
No spread means all values identical.
Q18. Mean of random variable depends on:
Answer: C) Both
Mean = Σ xP(x).
Mean = Σ xP(x).
Q19. Variance formula is:
Answer: B
Standard variance identity.
Standard variance identity.
Q20. If E(X) = 2 and E(X²) = 10, variance equals:
Answer: A) 6
Variance = 10 − 4 = 6.
Variance = 10 − 4 = 6.