Step-by-step explanation:
-17 < 3 - 5x
-3 -3 step 1: subtract 3 from both sides
-20 < -5x
/-5 /-5 step 2: divide both sides by 5
4 < x
An ellipse is divided into two axes, the longer axis is the
major axis and the shorter axis is the minor axis. The length of the major axis
of an ellipse is equal to the sum of two distance: the distance between any
point on the ellipse and one on focus and the distance between the same point
and the other focus. The focus is the point that helps define an ellipse and
every ellipse has two foci. These two distance are also called the red line
segment and blue line segment. Given 6 for red line segment and 4 for blue line
segment therefore, the length of the major axis of the ellipse is 10.
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: 9
Step-by-step explanation: Here, we have the expression <em>4x - 7</em> and we want to evaluate the expression when <em>x</em> is equal to 4.
To evaluate an expression, we simply plug the value
of the variable into the expression and solve.
So here, since <em>x</em> is equal to 4, we have 4(4) - 7.
4(4) is equal to 16.
So we have 16 - 7 which is equal to 9.
So the value of our expression when <em>x</em> is equal to 4 is 9.