Question

The following function is probability mass function. f left-parenthesis x right-parenthesis equals StartFraction 2x plus 1Over 25EndFraction comma x equals 0 comma 1 comma 2 comma 3 comma 4 Determine the mean, μ, and variance, σ2, of the random variable. Round your answers to two decimal places (e.g. 98.76).

Answer 1

Answer:

a) Mean  = 2.6

B) Variance = 9.2

Step-by-step explanation:

We are given the following probability mass function in the question:

$F(x) = \dfrac{2x+1}{25}, x = 0,1,2,3,4$

a) Mean of random variable

$\mu = \displaystyle\sum x_iF(x_i)\\\\=0(\dfrac{1}{25}) + 1(\dfrac{2+1}{25}) + 2(\dfrac{4+1}{25}) + 3(\dfrac{6+1}{25}) + 4(\dfrac{8+1}{25})\\\\=\dfrac{3+10+21+36}{25} = \dfrac{70}{25} = 2.8$

b) Variance of the random variable

$\sigma^2 = \displaystyle\sum x_i^2F(x_i)\\\\=0^2(\dfrac{1}{25}) + 1^2(\dfrac{2+1}{25}) + 2^2(\dfrac{4+1}{25}) + 3^2(\dfrac{6+1}{25}) + 4^2(\dfrac{8+1}{25})\\\\=\dfrac{3+20+63+144}{25} = \dfrac{230}{25} = 9.2$