A fair three-sided spinner has sides numbered 1, 2, 3. A fair five-sided spinner has sides numbered 1, 1, 2, 2, 3. Both spinners are spun once. For each spinner, the number on the side on which it lands is noted. The random variable $$\(X\)$$ is the larger of the two numbers if they are different, and their common value if they are the same. Find $$\(\mathrm{E}(X)\)$$ and $$\(\operatorname{Var}(X)\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_52 Year：2020 Question No：5(c)
Answer:
\(\mathrm{E}(X)=\frac{2+12+21}{15}=\frac{35}{15}=\frac{7}{3}\)
\(\operatorname{Var}(X)=\frac{1^{2} \times 2+2^{2} \times 6+3^{2} \times 7}{15}-\left(\frac{7}{3}\right)^{2}\)
\(\frac{22}{45}(0.489)\)
\(\operatorname{Var}(X)=\frac{1^{2} \times 2+2^{2} \times 6+3^{2} \times 7}{15}-\left(\frac{7}{3}\right)^{2}\)
\(\frac{22}{45}(0.489)\)
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)
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download