The probability distribution for a random variable x is given in the table X: -5,-3,-2,0,2,3 Probability: .17,.13,.33,.16,.11,.1
Ivan
Answer:
0.6 probability that ![-2 \leq x \leq 2](https://tex.z-dn.net/?f=-2%20%5Cleq%20x%20%5Cleq%202)
Step-by-step explanation:
The probability distribution is given in the table.
Probability that x is between -2 and 2.
Between -2 and 2, inclusive, we have -2, 0 and 2. So
![P(-2 \leq x \leq 2) = P(X = -2) + P(X = 0) + P(X = 2)](https://tex.z-dn.net/?f=P%28-2%20%5Cleq%20x%20%5Cleq%202%29%20%3D%20P%28X%20%3D%20-2%29%20%2B%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%202%29)
From the table:
. So
![P(-2 \leq x \leq 2) = P(X = -2) + P(X = 0) + P(X = 2) = 0.33 + 0.16 + 0.11 = 0.60](https://tex.z-dn.net/?f=P%28-2%20%5Cleq%20x%20%5Cleq%202%29%20%3D%20P%28X%20%3D%20-2%29%20%2B%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%202%29%20%3D%200.33%20%2B%200.16%20%2B%200.11%20%3D%200.60)
0.6 probability that ![-2 \leq x \leq 2](https://tex.z-dn.net/?f=-2%20%5Cleq%20x%20%5Cleq%202)
Answer:
25.12/8
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Answer:
a) ![y(t)=50000-49990e^{\frac{-2t}{25}}](https://tex.z-dn.net/?f=y%28t%29%3D50000-49990e%5E%7B%5Cfrac%7B-2t%7D%7B25%7D%7D)
b) ![31690.7 g/L](https://tex.z-dn.net/?f=31690.7%20g%2FL)
Step-by-step explanation:
By definition, we have that the change rate of salt in the tank is
, where
is the rate of salt entering and
is the rate of salt going outside.
Then we have,
, and
![R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}](https://tex.z-dn.net/?f=R_%7Bo%7D%3D40%5Cfrac%7BL%7D%7Bmin%7D%2A%5Cfrac%7By%7D%7B500%7D%20%5Cfrac%7Bg%7D%7BL%7D%3D%5Cfrac%7B2y%7D%7B25%7D%5Cfrac%7Bg%7D%7Bmin%7D)
So we obtain.
, then
, and using the integrating factor
, therefore
, we get
, after integrating both sides
, therefore
, to find
we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions
, so ![10= 50000+Ce^{\frac{-0*2}{25}}](https://tex.z-dn.net/?f=10%3D%2050000%2BCe%5E%7B%5Cfrac%7B-0%2A2%7D%7B25%7D%7D)
![10=50000+C\\C=10-50000=-49990](https://tex.z-dn.net/?f=10%3D50000%2BC%5C%5CC%3D10-50000%3D-49990)
Finally we can write an expression for the amount of salt in the tank at any time t, it is ![y(t)=50000-49990e^{\frac{-2t}{25}}](https://tex.z-dn.net/?f=y%28t%29%3D50000-49990e%5E%7B%5Cfrac%7B-2t%7D%7B25%7D%7D)
b) The tank will overflow due Rin>Rout, at a rate of
, due we have 500 L to overflow
, so we can evualuate the expression of a)
, is the salt concentration when the tank overflows
(-16/3, -5/3) is what I got