csat-suneung 2024 Q26

csat-suneung · South-Korea · csat__math 3 marks Discrete Probability Distributions Expectation and Variance from Context-Based Random Variables

When 4 coins are tossed simultaneously, let $X$ be the random variable representing the number of coins showing heads. Define the discrete random variable $Y$ as $$Y = \begin{cases} X & (\text{if } X \text{ takes the value } 0 \text{ or } 1) \\ 2 & (\text{if } X \text{ takes a value of } 2 \text{ or more}) \end{cases}$$ Find the value of $\mathrm{E}(Y)$. [3 points]
(1) $\frac{25}{16}$
(2) $\frac{13}{8}$
(3) $\frac{27}{16}$
(4) $\frac{7}{4}$
(5) $\frac{29}{16}$

When 4 coins are tossed simultaneously, let $X$ be the random variable representing the number of coins showing heads. Define the discrete random variable $Y$ as
$$Y = \begin{cases} X & (\text{if } X \text{ takes the value } 0 \text{ or } 1) \\ 2 & (\text{if } X \text{ takes a value of } 2 \text{ or more}) \end{cases}$$
Find the value of $\mathrm{E}(Y)$. [3 points]\\
(1) $\frac{25}{16}$\\
(2) $\frac{13}{8}$\\
(3) $\frac{27}{16}$\\
(4) $\frac{7}{4}$\\
(5) $\frac{29}{16}$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q23_calculus Q23_geometry Q24 Q24_calculus Q24_geometry Q25 Q25_calculus Q25_geometry Q26 Q26_calculus Q26_geometry Q27 Q27_calculus Q27_geometry Q28 Q28_calculus Q28_geometry Q29 Q29_geometry Q30 Q30_geometry