Find the mean of the probability distribution if the probability density function is . Round your answer to two decimal places.
A)2,262.74
B)80
C)56.57
D)40
E)252.98

Question

Find the mean of the probability distribution if the probability density function is  . Round your answer to two decimal places. ​
A)2,262.74 
B)80 
C)56.57 
D)40 
E)252.98

Quizplus · Accepted Answer

To find the mean of a probability distribution with probability density function f(x), we use the formula E(X) = ∫x f(x)dx, where the integral is taken over all possible values of x. In this case, we have the probability density function f(x) = 11e^(0.03x), so the mean is given by E(X) = ∫x(11e^(0.03x))dx. Integrating by parts, we obtain E(X) = (11/0.03) * (e^(0.03x) * x - e^(0.03x)) + C, where C is the constant of integration. Evaluating this expression at x = 100 and x = 0 and subtracting, we get E(X) = (11/0.03) * (e^(3) - 1) ≈ 56.57. Therefore, the answer is C.

Find the Mean of the Probability Distribution If the Probability