Elective Mathematics

Question 1

1For X ~ B(5, 0.5), P(X = 0) is

Easy

A. 0 B. 1/2 C. 1/5 D. 1/32

Question 2

2For X ~ B(4, 1/2), find P(X ≥ 3).

Hard

A. 1/4 B. 3/8 C. 11/16 D. 5/16

Question 3

3The sum of all probabilities in a probability distribution is

Easy

A. 1 B. 100 C. n D. 0

Question 4

4X follows a binomial distribution with n = 20 and p = 0.3. What is the variance of X?

Medium

A. 0.21 B. 6 C. 4.2 D. 14

Question 5

5A fair coin is tossed 4 times. P(exactly 2 heads) is

Medium

A. 1/16 B. 1/4 C. 1/2 D. 3/8

Question 6

6For a Poisson distribution with mean 2, P(X = 0) is

Hard

A. e⁻² B. 1/2 C. 2e⁻² D. 0

Question 7

7A discrete variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3. Find E(X).

Hard

A. 6 B. 1.5 C. 2 D. 2.1

Question 8

8For X ~ B(10, 0.3), the variance is

Easy

A. 2.1 B. 3 C. 0.21 D. 7

Question 9

9X follows a binomial distribution with n = 20 and p = 0.3. What is the mean of X?

Easy

A. 4.2 B. 14 C. 6 D. 0.3

Question 10

10For a binomial distribution B(n, p), the mean is

Easy

A. npq B. np C. p/n D. n/p