The probability density function of random variable \( X \) is given by: \[ f(x)=\left\{\begin{array}{cc}k e^{x+1}, & -2 \leq x \leq 2 ; \\ 0, & \text { otherwise. }\end{array}\right. \] Then \( k \) is equal to:

With probability (random) sampling techniques, each member of the population has an unequal chance of being selected for the research sample. Frue False

After a particular surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a special care ward (SCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day \( 4 \% \) of the patients in the ICU died, \( 51 \% \) were transferred to the SCW, and the remainder stayed in the ICU. Furthermore, each day \( 4 \% \) of the patients in the SCW developed complications and were returned to the ICU, \( 1 \% \) died while in the SCW, \( 22 \% \) were released from the hospital, and the remainder stayed in the SCW. A) In the long run, what percentage of the patients in the ICU are released from the hospital? \( 87.59 \% \) (Round to two decimal places as needed.) B) In the long run, what percentage of the patients in the SCW die without ever being released from the hospital? \% (Round to two decimal places as needed.)

After a particular surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a special care ward (SCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day \( 2 \% \) of the patients in the ICU died, \( 53 \% \) were transferred to the SCW, and the remainder stayed in the ICU. Furthermore, each day \( 4 \% \) of the patients in the SCW developed complications and were returned to the ICU, \( 1 \% \) died while in the SCW, \( 23 \% \) were released from the hospital, and the remainder stayed in the SCW. A) In the long run, what percentage of the patients in the ICU are released from the hospital? (Round to two decimal places as needed.)

a) 3 pts: Colauler \( P(A \cap B) \)

40. ¿Cuál es la probabilidad de que un equipo gane dos de sus partidos? Considere \( P(X=k ; n, p)=\left(\frac{n!}{k!(n-k)!}\right) \cdot p^{k} \cdot(1-p)^{n-k} \). A) 0.037 B) 0.111 C) 0.222 D) 0.250