IBDP Mathematics Question Analysis Topic: Mathematics - Probability
Exam Question:
Two numbers are selected at random(without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and variance of X.
Answer:
For IBDP Mathematics, you should know:
Two numbers are selected in 5×4 = 20 ways.
Let P(X) be the probability of X as the larger number.
P(2) = 220 (where the combinations are (1,2) and (2,1))
P(3) = 420 (where the combinations are (1,3),(3,1),(3,2) and (2,3))
P(4) = 620 (where the combinations are (1,4),(4,1),(4,2),(2,4),(3,4) and (4,3))
P(5) = 820 (where the combinations are (1,5),(5,1),(5,2),(2,5),(3,5),(5,3),(5,4) and (4,5))
So,
mean =∑5i=2 X × P(X) = 4
variance =∑5i=2 X2 × P(X) − (∑5i=2 X ×P(X))2 = 17 − 16 = 1.
Work hard for your IBDP Mathematics examination!
End of analysis. Great!