Answer:
a) 0.96
b) 0.016
c) 0.018
d) 0.982
e) x = 2
Step-by-step explanation:
We are given with the Probability density function f(x)= 2/x^3 where x > 1.
<em>Firstly we will calculate the general probability that of P(a < X < b) </em>
         P(a < X < b) =   =
 =  
 
                             = ![2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx](https://tex.z-dn.net/?f=2%5B%20%5Cfrac%7Bx%5E%7B-3%2B1%7D%20%7D%7B-3%2B1%7D%5D%5E%7Bb%7D_a%20%20%20dx) { Because
    { Because ![\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%20x%5E%7Bn%7D%20dx%20%3D%20%5B%20%5Cfrac%7Bx%5E%7Bn%2B1%7D%20%7D%7Bn%2B1%7D%5D%5E%7Bb%7D_a) }
 }
                             = ![2[ \frac{x^{-2} }{-2}]^{b}_a](https://tex.z-dn.net/?f=2%5B%20%5Cfrac%7Bx%5E%7B-2%7D%20%7D%7B-2%7D%5D%5E%7Bb%7D_a) =
 = ![\frac{2}{-2} [ x^{-2} ]^{b}_a](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B-2%7D%20%5B%20x%5E%7B-2%7D%20%5D%5E%7Bb%7D_a) 
 
                             = ![-1 [ b^{-2} - a^{-2}  ]](https://tex.z-dn.net/?f=-1%20%5B%20b%5E%7B-2%7D%20-%20a%5E%7B-2%7D%20%20%5D) =
 =  
 
a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }
      Comparing with general probability we get,
      P(1 < X < 5) =  =
 =  = 0.96 .
 = 0.96 .
b) P(X > 8) = P(8 < X < ∞) = 1/ - 1/∞ = 1/64 - 0 = 0.016
 - 1/∞ = 1/64 - 0 = 0.016 
c) P(6 < X < 10) =  =
 =  = 0.018 .
 = 0.018 .
d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞) 
                                 =  + (1/
 + (1/ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
 - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
e) We have to find x such that P(X < x) = 0.75 ;
                ⇒  P(1 < X < x) = 0.75 
                ⇒   = 0.75
 = 0.75 
                ⇒   = 1 - 0.75 = 0.25
 = 1 - 0.75 = 0.25 
                ⇒   =
 =  ⇒
   ⇒  = 4 ⇒ x =
 = 4 ⇒ x =  
  
Therefore, value of x such that P(X < x) = 0.75 is 2.
 
        
             
        
        
        
Answer:
12i + 2
Step-by-step explanation:
Combine like terms.
-1 + 3 = 2
5i + 7i = 12i
12i + 2 is your answer.
~
 
        
             
        
        
        
The common factors for 20 is 1,5
25 is 1,5
40 is 1,5
GCF:5
        
             
        
        
        
option 2. it increases 
because as x decrease 5/x will increase which will overall increase the expression value
 
        
             
        
        
        
Answer:0.32 is closer the the number one then 0.102 is
Step-by-step explanation: