Question

Directions: Please be sure to show all of your work, define your variables, give brief statements for all theoretical questions. Let X be a random variable with probability distribution $f(x)$. The mean, or expected value, of X is $\mu = E(X) = \sum_x x f(x)$ if X is discrete, and $\mu = E(X) = \int_{-\infty}^{\infty} x f(x) dx$ if X is continuous. Question 1 The probability distribution of the discrete random variable X is found below. Find the mean of X. (write answer as a decimal) $f(x) = \binom{3}{x} \left(\frac{1}{4}\right)^x \left(\frac{3}{4}\right)^{3-x}$, $x = 0, 1, 2, 3.$

          Directions: Please be sure to show all of your work, define your variables, give brief statements for all theoretical questions.
Let X be a random variable with probability distribution $f(x)$. The mean, or expected value, of X is
$\mu = E(X) = \sum_x x f(x)$
if X is discrete, and
$\mu = E(X) = \int_{-\infty}^{\infty} x f(x) dx$
if X is continuous.
Question 1
The probability distribution of the discrete random variable X is found below. Find the mean of X. (write answer as a decimal)
$f(x) = \binom{3}{x} \left(\frac{1}{4}\right)^x \left(\frac{3}{4}\right)^{3-x}$, $x = 0, 1, 2, 3.$

Directions: Please be sure to show all of your work, define your variables, give brief statements for all theoretical questions.
Let X be a random variable with probability distribution f(x). The mean, or expected value, of X is
μ = E(X) = x f(x)
if X is discrete, and
μ = E(X) = ∫-∞^∞ x f(x) dx
if X is continuous.
Question 1
The probability distribution of the discrete random variable X is found below. Find the mean of X. (write answer as a decimal)
f(x) = 3x((1)/(4))^x ((3)/(4))^3-x, x = 0, 1, 2, 3.

Added by Tracy H.

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