2. Una variable aleatoria continua \( X \) tiene la siguien- te función de densidad \[ f(x)=\left\{\begin{array}{ll}e^{-x} & x>0 \\ 0 & \text { en otro caso. }\end{array}\right. \] Calcule el valor esperado de \( g(X)=e^{2 n} \)

El \( 25 \% \) de los habitantes de una villa de 200 personas son jubilados, otro \( 25 \% \) son estudiantes. Si al \( 80 \% \) de los jubilados, al \( 10 \% \) de los estudiantes y al \( 20 \% \) del resto de la población les gusta la música clásica, entonces, la probabilidad de que elegida una persona al azar le guste éste tipo de música es

A card is drown at random from a pack of 52 playing conds. Rind the probability that the cord drawn is noither an ace nor a king.

What does it mean for two events to be independent in probability?

(b) From Salma's results, compute the experimental probability of landing on black. (c) Assuming that the spinner is fair, choose the statement below that is true: The experimental and theoretical probabilities must always be equal. As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.

What are dependent events in probability?