IBDP Mathematics Question Analysis - Mathematics - Probability

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.

$\mathrm{Let\; P(X)\; be\; the\; probability\; of\; X\; as\; the\; larger\; number.}$

$P(2)\; =\; 220\; (where\; the\; combinations\; are\; (1,2)\; and\; (2,1))$

$P(3)\; =\; 420\; (where\; the\; combinations\; are\; (1,3),(3,1),(3,2)\; and\; (2,3))$

$P(4)\; =\; 620\; (where\; the\; combinations\; are\; (1,4),(4,1),(4,2),(2,4),(3,4)\; and\; (4,3))$

$P(5)\; =\; 820\; (where\; the\; combinations\; are\; (1,5),(5,1),(5,2),(2,5),(3,5),(5,3),(5,4)\; and\; (4,5))$

$So,mean\; =\sum 5i=2\; X\; \times \; P(X)\; =\; 4variance\; =\sum 5i=2\; X2\; \times \; P(X)\; -\; (\sum 5i=2\; X\; \times P(X))2\; =\; 17\; -\; 16\; =\; 1.$

Work hard for your IBDP Mathematics examination!

End of analysis. Great!

CLICK HERE TO LEARN MORE ABOUT OUR IBDP MATHEMATICS COURSES!