Seja X uma vari´avel aleat´oria cont´ınua com fun¸c˜ao de densidade f(x) =
ax se 0 ≤ x ≤ 1

a se 1 ≤ x ≤ 2

3a − ax se 2 ≤ x ≤ 3

0 em outro caso

onde a ´e uma constante.

(a) (0,6 pts.) Encontre o valor da constante a.

(b) (0,4 pts.) Calcule a esperan¸ca de X.

(c) (1,6 pts.) Seja X1, X2, X3 uma amostra independente de tamanho trˆes. Qual a

probabilidade de que exatamente um dos elementos dessa amostra seja maior do que

0, 9+0, 1k, onde k ´e igual 23

If n stands for number sold and c stands for cost per item, in which column would you use the formula: ? a. column d c. column f b. column e d. column g

Solve the following inequalities and show the solution on a number line. 2x+3< 3(4x+5)

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?