Answer:
1.3125
Step-by-step explanation:
Given that our random variable
follows a Poisson distribution![P(X=k)=\frac{\lambda^k e^-^p}{k!} \ \ \ \ \ \ \ \ p=\lambda](https://tex.z-dn.net/?f=P%28X%3Dk%29%3D%5Cfrac%7B%5Clambda%5Ek%20e%5E-%5Ep%7D%7Bk%21%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20p%3D%5Clambda)
Evaluate the formula at ![k=2,3:](https://tex.z-dn.net/?f=k%3D2%2C3%3A)
![P(X=2)=0.5\lambda^2e^{-\lambda}\\\\P(X=3)=\frac{1}{6}\lambda^2e^{-\lambda}](https://tex.z-dn.net/?f=P%28X%3D2%29%3D0.5%5Clambda%5E2e%5E%7B-%5Clambda%7D%5C%5C%5C%5CP%28X%3D3%29%3D%5Cfrac%7B1%7D%7B6%7D%5Clambda%5E2e%5E%7B-%5Clambda%7D)
#since
![4P(X=2)=P(X=3);\\\\0.5\lambda^2e^{-\lambda}=4\times\frac{1}{6}\lambda^3e^{-\lambda}\\\\0.5\lambda^2=\frac{2}{3}\lambda^3\\\\0.75=\lambda](https://tex.z-dn.net/?f=4P%28X%3D2%29%3DP%28X%3D3%29%3B%5C%5C%5C%5C0.5%5Clambda%5E2e%5E%7B-%5Clambda%7D%3D4%5Ctimes%5Cfrac%7B1%7D%7B6%7D%5Clambda%5E3e%5E%7B-%5Clambda%7D%5C%5C%5C%5C0.5%5Clambda%5E2%3D%5Cfrac%7B2%7D%7B3%7D%5Clambda%5E3%5C%5C%5C%5C0.75%3D%5Clambda)
The mean and variance of the Poisson distributed random variable is equal to
:
![\mu=\lambda=0.75\\\sigma ^2=\lambda=0.75](https://tex.z-dn.net/?f=%5Cmu%3D%5Clambda%3D0.75%5C%5C%5Csigma%20%5E2%3D%5Clambda%3D0.75)
#By property variance:
![\sigma ^2=V(X)=E(X^2)-(E(X))^2=E(X^2)\\\\E(X^2)=\sigma^2+\mu^2=0.75+0.75^2=1.3125](https://tex.z-dn.net/?f=%5Csigma%20%5E2%3DV%28X%29%3DE%28X%5E2%29-%28E%28X%29%29%5E2%3DE%28X%5E2%29%5C%5C%5C%5CE%28X%5E2%29%3D%5Csigma%5E2%2B%5Cmu%5E2%3D0.75%2B0.75%5E2%3D1.3125)
The expectation is 1.3125
Answer:
1445.6 hours
Step-by-step explanation:
Distance between New York and San Francisco = 2902.8 miles (checked online)
Average speed of car = 2 mi/hr
Average speed of jet = 500 mi/hr
Time taken by Jet:
Time taken = Distance / speed
Time taken = 2902.8 / 500
Time taken = 5.8056 = 5.8 hours
Time taken by Car :
Time taken = Distance / speed
Time taken = 2902.8 / 2
Time taken = 5.8056 = 1451.4 hours
Time difference :
1451.4 - 5.8 = 1445.6 hours
The first 6 is equal to 6,000. The second 6 is equal to 600. 6,000 is 10 times greater than 600.
Hope this Helps!
Answer:
3,200
Step-by-step explanation:
you would have to multiply then estimate wich round it down an dyou get 3,200
(0,0),(2,16)
slope = (16 - 0) / (2 - 0) = 16/2 = 8
y = mx + b
slope(m) = 8
and since the line goes thru the origin, the y int is 0
in y = mx + b form, the slope is in the m position and the y int is n the b position....so ur equation is :
y = 8x + 0 which can be written as y = 8x <==