A/78 = 25/100 . . . . the equation
a = 78*25/100 = 19.5
19.5 is 25% of 78
        
             
        
        
        
Answer and Explanation:
Given : The random variable x has the following probability distribution.
To find : 
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x. 
c. Calculate the variance of x. 
d. Calculate the standard deviation of x.
Solution : 
First we create the table as per requirements,
x      P(x)         xP(x)           x²            x²P(x)
0    0.25           0               0                0
1     0.20        0.20             1              0.20
2    0.15          0.3               4             0.6
3    0.30         0.9               9             2.7
4    0.10          0.4               16             1.6
    ∑P(x)=1     ∑xP(x)=1.8               ∑x²P(x)=5.1
a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.


Yes it is a probability distribution.
b) The expected value of x is defined as

c) The variance of x is defined as 

d) The standard deviation of x is  defined as 



 
        
             
        
        
        
Answer:
h=A-2πr2/2πr
Step-by-step explanation:
 
        
             
        
        
        

Let the capacity of bus be x students 
And van be y students, now ;
From the given statements we get two equations ~ 


multiply the equation (2) with 2 [ it won't change the values ]


Now, deduct equation (1) from equation (3)




Therefore each bus can carry (x) = 45 students
Now, plug the value of x in equation (1) to find y ~







Hence, each van can carry (y) = 17 students in total.