+ √6 = √9
The first step is to get
by itself. We can do this by subtracting
from each side, and simplifying 
= 3 - 
Now we square both sides
5x = (3 -
)²
Using the formula (a - b)² = a² -2ab + b², (3 -
)² = 15 - 6
5x = 15 - 6
x = 
Answer:
Step-by-step explanation:
<u>Given expression</u>
<u>Solving for x</u>
- 4px + 4 = 64
- 4px = 60
- px = 15
- x = 15/p
<u>Value of x when p= - 5</u>
Answer:
m=9n
Step-by-step explanation:
Linear equation, straight forward m=3n. Highlighted point is n=3 and m=9*3=27
The question is incomplete. The complete question is :
Let X be a random variable with probability mass function
P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6
(a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5). You answer should give at least the values g(k) for all possible values of k of X, but you can also specify g on a larger set if possible.
(b) Let t be some real number. Find a function g such that E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)
Solution :
Given :

a). We know :
![$E[g(x)] = \sum g(x)p(x)$](https://tex.z-dn.net/?f=%24E%5Bg%28x%29%5D%20%3D%20%5Csum%20g%28x%29p%28x%29%24)
So, 

Therefore comparing both the sides,


Also, 
b).
We known that ![$E[g(x)] = \sum g(x)p(x)$](https://tex.z-dn.net/?f=%24E%5Bg%28x%29%5D%20%3D%20%5Csum%20g%28x%29p%28x%29%24)
∴ 

Therefore on comparing, we get

∴ 