Respuesta :
Answer:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74[/tex]In order to find the variance we need to calculate first the second moment given by:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36[/tex]And the variance is given by:
[tex] Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924[/tex]
And the deviation would be:
[tex] Sd(X) =\sqrt{0.8924} =0.9447[/tex]
Step-by-step explanation:
Previous concepts
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).
Solution to the problem
For this case we have the following distribution given:
X 3 4 5 6
P(X) 0.07 0.4 0.25 0.28
We can calculate the mean with the following formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74[/tex]
In order to find the variance we need to calculate first the second moment given by:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36[/tex]
And the variance is given by:
[tex] Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924[/tex]
And the deviation would be:
[tex] Sd(X) =\sqrt{0.8924} =0.9447[/tex]
