Answer:
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
