An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained. On another occasion, this die is thrown 3 times. The random variable $$$X$$$ is the number of times that a 1 or a 6 is obtained. Find $$$\mathrm{E}(X)$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m20_qp_52 Year：2020 Question No：2(c)

Answer:

$\mathrm{E}(X)=\left[0 \times \frac{8}{27}\right]+1 \times \frac{12}{27}+2 \times \frac{6}{27}+3 \times \frac{1}{27}$
$=\left[\frac{0}{27}\right]+\frac{12}{27}+\frac{12}{27}+\frac{3}{27}$
$=1$

Knowledge points:

5.4.1 draw up a probability distribution table relating to a given situation involving a discrete random variable X, and calculate E(X) and Var(X)

Answer:

Knowledge points:

Solution:

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