Answer:
[tex] 22.1 = 1*0.1 +10*0.1 +15*0.1 + 20*0.1 +25*0.1 + x*0.5[/tex]
And we can solve for the value of x and we got:
[tex] 22.1 -[1*0.1 +10*0.1 +15*0.1 + 20*0.1 +25*0.1 ] = 0.5 x[/tex]
[tex]15 = 0.5 x[/tex]
[tex] x =30.0[/tex]
Step-by-step explanation:
For this case we have the following distribution:
X 1 10 15 20 25 x
P(X) 0.1 0.1 0.1 0.1 0.1 0.5
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
The expected value is given by:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]
And replacing we have this:
[tex] 22.1 = 1*0.1 +10*0.1 +15*0.1 + 20*0.1 +25*0.1 + x*0.5[/tex]
And we can solve for the value of x and we got:
[tex] 22.1 -[1*0.1 +10*0.1 +15*0.1 + 20*0.1 +25*0.1 ] = 0.5 x[/tex]
[tex]15 = 0.5 x[/tex]
[tex] x =30.0[/tex]
