3 years ago

Are all of these four right ? If not,plz help

Mathematics

1 answer:

abruzzese [7]3 years ago

6 0

I think 3 is actually 0

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The following function is probability mass function. f left-parenthesis x right-parenthesis equals StartFraction 2x plus 1Over 2

lora16 [44]

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

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