Answer:
a) Mean = 2.6
B) Variance = 9.2
Step-by-step explanation:
We are given the following probability mass function in the question:
[tex]F(x) = \dfrac{2x+1}{25}, x = 0,1,2,3,4[/tex]
a) Mean of random variable
[tex]\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[/tex]
b) Variance of the random variable
[tex]\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[/tex]
