Answer: 33
Step-by-step explanation: The ratio is 4:7, so the number has to be a multiple of 11, and the multiple of 11 between 24 and 40 is 33.
Answer:
a) P ( 3 ≤X≤ 5 ) = 0.02619
b) E(X) = 1
Step-by-step explanation:
Given:
- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:
Find:
a.Calculate the probability that 3 ≤X≤ 5
b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that
Solution:
- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.
![F(X) = P ( 3=](https://tex.z-dn.net/?f=F%28X%29%20%3D%20P%20%28%203%3D%3CX%20%3D%3C%205%29%20%3D%20%5B1%20-%20%5Cfrac%7B1%7D%7B%28x%2B1%29%2A%28x%2B2%29%7D%5D%5Climits%5E5_3%5C%5C%5C%5CF%28X%29%20%3D%20P%20%28%203%3D%3CX%20%3D%3C%205%29%20%3D%20%5B-%5Cfrac%7B1%7D%7B%285%2B1%29%2A%285%2B2%29%7D%20%2B%20%5Cfrac%7B1%7D%7B%283%2B1%29%2A%283%2B2%29%7D%7D%5C%5C%5C%5CF%28X%29%20%3D%20P%20%28%203%3D%3CX%20%3D%3C%205%29%20%3D%20%5B-%5Cfrac%7B1%7D%7B%2842%29%7D%20%2B%20%5Cfrac%7B1%7D%7B%2820%29%7D%7D%5D%5C%5C%5C%5CF%28X%29%20%3D%20P%20%28%203%3D%3CX%20%3D%3C%205%29%20%3D%200.02619)
- The Expected Value can be determined by sum to infinity of CDF:
E(X) = Σ ( 1 - F(X) )
![E(X) = \frac{1}{(x+1)*(x+2)} = \frac{1}{(x+1)} - \frac{1}{(x+2)} \\\\= \frac{1}{(1)} - \frac{1}{(2)}\\\\= \frac{1}{(2)} - \frac{1}{(3)} \\\\= \frac{1}{(3)} - \frac{1}{(4)}\\\\= ............................................\\\\= \frac{1}{(n)} - \frac{1}{(n+1)}\\\\= \frac{1}{(n+1)} - \frac{1}{(n+ 2)}](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%5Cfrac%7B1%7D%7B%28x%2B1%29%2A%28x%2B2%29%7D%20%3D%20%5Cfrac%7B1%7D%7B%28x%2B1%29%7D%20-%20%5Cfrac%7B1%7D%7B%28x%2B2%29%7D%20%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B%281%29%7D%20-%20%5Cfrac%7B1%7D%7B%282%29%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B%282%29%7D%20-%20%5Cfrac%7B1%7D%7B%283%29%7D%20%5C%5C%5C%5C%3D%20%20%5Cfrac%7B1%7D%7B%283%29%7D%20-%20%5Cfrac%7B1%7D%7B%284%29%7D%5C%5C%5C%5C%3D%20............................................%5C%5C%5C%5C%3D%20%20%5Cfrac%7B1%7D%7B%28n%29%7D%20-%20%5Cfrac%7B1%7D%7B%28n%2B1%29%7D%5C%5C%5C%5C%3D%20%20%5Cfrac%7B1%7D%7B%28n%2B1%29%7D%20-%20%5Cfrac%7B1%7D%7B%28n%2B%202%29%7D)
E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]
E(X) = 1
Answer:
La altura de Juan por lo tanto es de 1.6 metros de altura
Step-by-step explanation:
Segun los datos que se encuentran en el ejercicio, tenemos lo siguiente:
Juan proyecta una sombra de 2 metros en el momento en que Pedro que mide 1,80.
Supongamos que x es la altura de juan que tenemos que calcular.
La altura de Juan por lo tanto la podemos calcular de la siguiente manera con la siguiente formula:
x= (1.8 metros/2.25 metros)*2
x=1.6 metros
La altura de Juan por lo tanto es de 1.6 metros de altura
Answer:
1 dollar is equal to 0.75 E
Step-by-step explanation:
120$ = 90 e -----> 4$ = 3E
250$ = 187.50 e -----> 4$ = 3E
400$ = 300 e -----> 4$ = 3E
----------------------------------
from this we know 4$ = 3E
1 E = 4$/3
1 E = 1.33...$
---------------------
1 $ = 3/4 E
1 $ = 0.75 E
---------------------
1.33...$ dollars is equal to 1 E and
1 $ is equal to 0.75 E
-----------------------------------
90 x 1.33... =120
187.50x1.33...= 250
300 x 1.33... = 400
--------------------------
72 square centimeters because
<span>(12×10)−(8×6)</span>
<span>120−48</span>
<span>72</span>