Determine the mean and variance of the random variable with the following probability mass function. f (x) = (216/43) (1/6) ^x, x = 1, 2, 3 Round your answers to three decimal places (e. g. 98.765). Mean = Variance =

The mean of function provided is 1.186.

The variance of the provided f (x) is 0.198

Step-by-step explanation:

It is provided that the probability mass function is,

f (x) = (214/43) * (1/6) ˣ; x=1,2,3

The mean is calculated as,

E (X) = ∑ x * f (x)

x

=1 * (216/43) * (1/6) ¹ + 2 * (216/43) * (1/6) ² * 3 * (216/43) * (1/6) ³

=36/43 + 12/43 + 3/43

= 1.186



The mean of function provided is 1.186

Explanation | Common mistakes | Hint for next step

The expected value of the probability mass function, f (x) = (216/43 * (1/6) ˣ

is 1.1861.186.

Step 2 of 2

To calculate the variance, first calculate E (X²) = ∑ x² * f (x)

= 1² * (216/43) * (1/6) ¹ + 2² * (216/43) * (1/6) ² * 3² * (216/43) * (1/6) ³

=36/43 + 24/43 + 9/43

=1.605



The variance is calculated as,

V (X) = E (X²) - [E (X) ]²

=1.605 - (1.186) ²

= 0.198

The variance of the provided f (x) is 0.198

Explanation | Common mistakes

The variance of function f (x) = (216/43) * (1/6) ˣ; x = 1,2,3 is 0.198