Question

Assume that you assign the following subjective probabilities for your final grade in your econometrics course (the standard GPA scale of 4-A to 0-F applies): Probability 0.20 0.50 0.20 0.08 0.02 Grade The expected value is_____________.A. 3.5 B. 3.25. C. 2.78.D. 3.0

Answer 1

Answer:

$E(X) = 4*0.2 +3*0.5+ 2*0.2 +1*0.8+ 0*0.02= 2.78$

So then the best answer for this case would be:

C. 2.78

Step-by-step explanation:

For this case we have the following probabability distribution function given:

Score         P(X)

A= 4.0       0.2

B= 3.0       0.5

C= 2.0       0.2

D= 1.0        0.08

F= 0.0       0.02

______________

Total          1.00

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.

If we use the definition of expected value given by:

$E(X) = \sum_{i=1}^n X_i P(X_I)$

And if we replace the values that we have we got:

$E(X) = 4*0.2 +3*0.5+ 2*0.2 +1*0.8+ 0*0.02= 2.78$

So then the best answer for this case would be:

C. 2.78